CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
CALCULUS EARLY TRANSCENDENTAL FUNCTIONS
7th Edition
ISBN: 9781337678445
Author: Larson, Edward
Publisher: CENGAGE L
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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…
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Chapter 6.3, Problem 21E

Finding a Particular Solution Using Separation of Variables III Exercises 17-26, find the particular solution of the differential equation that satisfies the initial condition.

Differential EquationInitial Condition

y ( 1 + x 2 ) y ' − x ( 1 + y 2 ) = 0 y ( 0 ) = 3

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Tutorial Exercise Consider the differential equation x²y" - 4xy' + 6y=0; x², x³², (0, on). Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval. Form the general solution. Step 1 We are given the following homogenous differential equation and pair of solutions on the given interval. x²y" - 4xy + 6y=0; x², x³, (0, 0) We are asked to verify that the solutions are linearly independent. That is, there do not exist constants c, and c₂, not both zero, s are different powers of x, we have a formal test to verify the linear independence. Recall the definition of the Wronskian for the case of two functions f, and f, each of which have a first derivative. f₂ W(f₁, f₂) = Will HOUTBEave any pronTIES FOR LA By Theorem 4.1.3, if W(f₁, f₂) 0 for every x in the interval of the solution, then solutions are linearly independent. Let f(x) = x² and f(x) = x³. Complete the Wronskian for these functions. x² w(x², x³) = 2x
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Differential Equations: Find the general solution

Chapter 6 Solutions

CALCULUS EARLY TRANSCENDENTAL FUNCTIONS

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Prob. 83ECh. 6.1 - Prob. 84ECh. 6.1 - Prob. 85ECh. 6.1 - Prob. 86ECh. 6.1 - Prob. 87ECh. 6.1 - Prob. 88ECh. 6.1 - Prob. 89ECh. 6.1 - Prob. 90ECh. 6.1 - Prob. 91ECh. 6.1 - Slope Field A slope field shows that the slope at...Ch. 6.1 - Prob. 93ECh. 6.1 - Prob. 94ECh. 6.1 - Prob. 95ECh. 6.1 - Prob. 96ECh. 6.2 - CONCEPT CHECK Describing Values Describe what the...Ch. 6.2 - Prob. 2ECh. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - Solving a Differential Equation In Exercises 3-12,...Ch. 6.2 - 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Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay In Exercises 29-36, complete the...Ch. 6.2 - Radioactive Decay Radioactive radium has a...Ch. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Prob. 42ECh. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Prob. 46ECh. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Population In Exercises 51-54, the population (in...Ch. 6.2 - Population In Exercises 51-54, the population (in...Ch. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Bacteria Growth The number of bacteria in a...Ch. 6.2 - Prob. 57ECh. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Forestry The value of a tract of timber is...Ch. 6.2 - Prob. 63ECh. 6.2 - Prob. 64ECh. 6.2 - Newton's Law of Cooling When an object is removed...Ch. 6.2 - Newton's Law of Cooling A container of hot liquid...Ch. 6.2 - 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