Problem 19. Consider the differential equation y =f(x), where the graph of the function f is shown below. Use this graphto construct a slope field for this differential equation, then use your slope field to approximate the graph of the solution whichpasses through the point (-1,1) and the solution which passes through the point -4,-1).y-5.0-4.5-4.0-3.5-3.0-2.5-2.0-1.5-1.0-0.50,5X-2-4-6-8

We have to sketch the slope field of the differential equation y'=fx and then we will sketch the…

Answered: Problem 19. Consider the differential…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Bob starts working at age 20 and his pay is $15,000 a year. Over the next 10 years he receives pay raises which are proportional to √2t, where t is measured in years. Which equation below describes the correct differential equation to model this change in his Bob's pay, P(t)? dP = k√√/2t dt dP = 2t + C dt dP = dt dP = √2t dt √2t + C
FOR PART C, can you explain how they got the quadratic equation
Newton's Law of Cooling states that the rate at which the temperature of a cooling object decreases and the rate at which a warming object increases are proportional to the difference between the temperature of the object and the temperature of the surrounding medium. The differential equation formula is given as: dT = k (T – A) dt - T = temperature of object at time t А ambient temperature (aka temperature of the surrounding medium) k = constant of proportionality Okay, now here's the problem. A glass of delicious orange soda (with an initial temperature of 34°F) is placed in a room with a constant temperature of 72°F. One hour later, the temperature of the orange soda is 52°F. Find the exact simplified value of k. Hint: solve the differential equation for T and note that A is a constant.
SHow and explain all steps
Part d please
For this problem T is the variable for the temperature, k is the growth constant (or constant of proportionality) and is positive.Newton's Law of cooling states that the temperature of an object changes at a rate proportional to the difference of the temperature of the surrounding medium and the temperature of the object. If the temperature of the surrounding medium is 340∘� write a differential equation to model the situation.
Q8a needed
A particle moves along x - axis and the differential equation governing the motion of the particle by Newton's Law is given by d²x d₁² = - 16x 16- dx dt Find an expression for the position x of the particle as a function of time t if the particle is initially at rest at x = 10 units. O x = e-2t(1+20t) O x = e-2t(10+2t) 10e-2t (1+2t) X = O x = 10e²t(1+2t)

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