Explanation Given Information: In the begin of a chemical reaction amount of the original compound was 27grams and amount left after 1hour in a chemical reaction is 8gram and compound changes into another compound at rate of proportional to cube root of unchanged amount y . Formula used: Steps to find the particular solution of a given differential equation are as: Step 1: Form a differential equation from the given condition. Step 2: Solve the differential equation for general solution of differential equation. Step 3: Using initial condition find the value of c Step 4: Using another condition find the value of k Step 5: Substituting the values of c and k in general solution get particular solution. Calculation: Now consider the provided information as, In the begin of a chemical reaction amount of the original compound was 27grams and amount left after 1hour in a chemical reaction is 8gram and compound changes into another compound at rate of proportional to cube root of unchanged amount y . Here unchanged amount of chemical is y. The rate of change in another compound is d y d t . Now, rate of change is proportional to cube root of the unchanged amount. d y d t α y 1 3 d y d t = k y 1 3 Rearranging the above equation, d y y 1 3 = k d t Integrating on both sides, ∫ d y y 1 3 = ∫ k d t y 2 3 ( 2 3 ) = k t + c Substitute the initial conditions t = 0 hours , y = 27 grams in above equation, ( 27 )

10th Edition

ISBN: 8220101426222

Author: Larson

Publisher: CENGAGE L

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 11, Problem 71RE

To determine

To calculate: The particular solution if in the begin of a chemical reaction amount of the original compound was 27grams and amount left after 1hour in a chemical reaction is 8gram.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 70RE

Chapter 11, Problem 72RE

Students have asked these similar questions

Please solve this Chemical Mixture Problem (Differential Equation) and provide a complete solution. A tank contains 1000 liters of brine with 15 kg of dissolved salt. Pure water enters the tank at a rate of 10 liters per minute. The solution is kept thoroughly mixed and drains from the tank at the same rate. How much salt is in the tank after t minutes?

use linear differential equation

Solve the differential equation 4yp2-2px-y=0

Chapter 11 Solutions

EBK CALCULUS: AN APPLIED APPROACH

Ch. 11.1 - Checkpoint 1 Worked-out solution available at...Ch. 11.1 - Prob. 2CP Ch. 11.1 - Prob. 3CP Ch. 11.1 - Prob. 4CP Ch. 11.1 - Prob. 1SWU Ch. 11.1 - Prob. 2SWU Ch. 11.1 - Prob. 3SWU Ch. 11.1 - Prob. 4SWU Ch. 11.1 - Prob. 5SWU Ch. 11.1 - Prob. 6SWU

Ch. 11.1 - Verifying Solutions In Exercises 112, verify the...Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Verifying Solutions In Exercises 1-12, verify the...Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Determining Solutions In Exercises 1316, determine...Ch. 11.1 - Prob. 16E Ch. 11.1 - Determining Solutions In Exercises 1720, determine...Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Investment The rate of growth of an investment is...Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.2 - Checkpoint 1 Worked-out solution available at...Ch. 11.2 - Prob. 2CP Ch. 11.2 - Prob. 3CP Ch. 11.2 - Prob. 4CP Ch. 11.2 - Prob. 5CP Ch. 11.2 - Prob. 6CP Ch. 11.2 - Prob. 1SWU Ch. 11.2 - Prob. 2SWU Ch. 11.2 - Prob. 3SWU Ch. 11.2 - Prob. 4SWU Ch. 11.2 - Prob. 5SWU Ch. 11.2 - Prob. 6SWU Ch. 11.2 - Prob. 7SWU Ch. 11.2 - Prob. 8SWU Ch. 11.2 - Prob. 9SWU Ch. 11.2 - Prob. 10SWU Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Solving a Differential Equation In Exercises 7-26,...Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 33E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 35E Ch. 11.2 - Finding a Particular Solution In Exercises 31-38,...Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Radioactive Decay The rate of decomposition of...Ch. 11.2 - Solve the differential equation. Weight Gain A...Ch. 11.2 - Prob. 1QY Ch. 11.2 - Prob. 2QY Ch. 11.2 - Prob. 3QY Ch. 11.2 - Prob. 4QY Ch. 11.2 - Prob. 5QY Ch. 11.2 - Prob. 6QY Ch. 11.2 - Prob. 7QY Ch. 11.2 - Prob. 8QY Ch. 11.2 - Prob. 9QY Ch. 11.2 - Prob. 10QY Ch. 11.2 - Prob. 11QY Ch. 11.2 - Prob. 12QY Ch. 11.2 - Prob. 13QY Ch. 11.2 - Prob. 14QY Ch. 11.2 - Prob. 15QY Ch. 11.2 - Ignoring resistance, a sailboat starting from rest...Ch. 11.3 - Checkpoint 1 Worked-out solution available at...Ch. 11.3 - Prob. 2CP Ch. 11.3 - Prob. 3CP Ch. 11.3 - Prob. 1SWU Ch. 11.3 - Prob. 2SWU Ch. 11.3 - Prob. 3SWU Ch. 11.3 - Prob. 4SWU Ch. 11.3 - Prob. 5SWU Ch. 11.3 - Prob. 6SWU Ch. 11.3 - Prob. 7SWU Ch. 11.3 - Prob. 8SWU Ch. 11.3 - In Exercises 5-10, find the indefinite integral....Ch. 11.3 - Prob. 10SWU Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 10E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Prob. 17E Ch. 11.3 - Solving a Linear Differential Equation In...Ch. 11.3 - Using Two Methods In Exercises 19-22, solve for y...Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Finding a Particular Solution In Exercises 27-34,...Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Vertical Motion A falling object encounters air...Ch. 11.3 - Velocity A booster rocket carrying an observation...Ch. 11.3 - Learning Curve The management at a medical supply...Ch. 11.3 - Investment Let A he the amount in a fund earning...Ch. 11.4 - Prob. 1CP Ch. 11.4 - Prob. 2CP Ch. 11.4 - Checkpoint 3 Worked-out solution available at...Ch. 11.4 - Prob. 4CP Ch. 11.4 - Checkpoint 5 Worked-out solution available at...Ch. 11.4 - Prob. 1SWU Ch. 11.4 - Prob. 2SWU Ch. 11.4 - Prob. 3SWU Ch. 11.4 - Prob. 4SWU Ch. 11.4 - Prob. 5SWU Ch. 11.4 - Prob. 6SWU Ch. 11.4 - Prob. 7SWU Ch. 11.4 - Prob. 8SWU Ch. 11.4 - Prob. 9SWU Ch. 11.4 - Prob. 10SWU Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Advertising Awareness In Exercises 3 and 4, use...Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Chemistry A wet towel hung from a clothesline to...Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Biology A population of eight beavers has been...Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Chemical Mixture A 100-gallon tank is full of a...Ch. 11.4 - Chemical Mixture A 200-gallon tank is half full of...Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Finding a Particular Solution In Exercises 15 and...Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 39RE Ch. 11 - Prob. 40RE Ch. 11 - Prob. 41RE Ch. 11 - Solving a Differential Equation In Exercises...Ch. 11 - Prob. 43RE Ch. 11 - Prob. 44RE Ch. 11 - Prob. 45RE Ch. 11 - Prob. 46RE Ch. 11 - Prob. 47RE Ch. 11 - Prob. 48RE Ch. 11 - Prob. 49RE Ch. 11 - Prob. 50RE Ch. 11 - Prob. 51RE Ch. 11 - Prob. 52RE Ch. 11 - Prob. 53RE Ch. 11 - Prob. 54RE Ch. 11 - Prob. 55RE Ch. 11 - Prob. 56RE Ch. 11 - Solving a Linear Differential Equation In...Ch. 11 - Prob. 58RE Ch. 11 - Prob. 59RE Ch. 11 - Prob. 60RE Ch. 11 - Prob. 61RE Ch. 11 - Prob. 62RE Ch. 11 - Prob. 63RE Ch. 11 - Prob. 64RE Ch. 11 - Prob. 65RE Ch. 11 - Prob. 66RE Ch. 11 - Safety Assume the rate of change per hour in the...Ch. 11 - Prob. 68RE Ch. 11 - Prob. 69RE Ch. 11 - Prob. 70RE Ch. 11 - Prob. 71RE Ch. 11 - Prob. 72RE Ch. 11 - Prob. 73RE Ch. 11 - Prob. 74RE Ch. 11 - Prob. 75RE Ch. 11 - Chemical Mixture A tank contains 30 gallons of a...Ch. 11 - Chemical Mixture A tank contains 20 gallons of a...Ch. 11 - Prob. 1TYS Ch. 11 - Prob. 2TYS Ch. 11 - Prob. 3TYS Ch. 11 - Prob. 4TYS Ch. 11 - Prob. 5TYS Ch. 11 - Prob. 6TYS Ch. 11 - Prob. 7TYS Ch. 11 - Prob. 8TYS Ch. 11 - Prob. 9TYS Ch. 11 - Prob. 10TYS Ch. 11 - Prob. 11TYS Ch. 11 - A lamb that weighs 10 pounds at birth gains weight...Ch. 11 - Prob. 13TYS

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The particular solution if in the begin of a chemical reaction amount of the original compound was 27grams and amount left after 1hour in a chemical reaction is 8gram .

Solution Summary: The author explains the formula used to find the particular solution of a given differential equation.

Concept explainers

Videos

To calculate: The particular solution if in the begin of a chemical reaction amount of the original compound was 27grams and amount left after 1hour in a chemical reaction is 8gram.

Want to see the full answer?

Chapter 11 Solutions