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Description: Question is in image provided Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful.xy" + y' = 60xThe general solution is y(x) =

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Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful. xy" + y' = 60x The general solution is y(x) =

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.CR: Chapter 11 Review

Problem 33CR

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Question is in image provided

Find the general solution of the following reducible second-order differential equation. Assume x, y and/or y' positive where helpful.
xy" + y' = 60x
The general solution is y(x) =

Expert Solution

Step 1

Given second order differential is

$x y^{''} + y^{'} = 60 x$

As $x & y$ are positive , then we can divide both sides in above by x.

That is ,

$y^{''} + \frac{1}{x} y^{'} = 60$ - (1)

Now let us assume $x = e^{z}$ or $z = \log x$ , then

$\begin{array}{rcl} \frac{d y}{d x} & = & \frac{d y}{d z} \cdot \frac{d z}{d x} \\ = & \frac{1}{x} \cdot \frac{d y}{d z} \end{array}$ $(∵ z = \log x)$

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