Can we solve the following ODE via reduction of order? $y''+y'''sin(y)=0$.

Mathematics Asked by Trevor Frederick on November 16, 2020

I am struggling with one problem in particular.

$y” + y”’sin(y) = 0$ is the equation.

I am told to let $y’ = z$ and do reduction of order to give:

$z’+z”sin(z)= 0$

But I am absolutely stuck. I don’t know what a possible solution would be to do reduction of order. I thought about $Acos(y) = z$ as a solution.

Any advice?

One Answer


With reference to,

Let $u=left(dfrac{dy}{dx}right)^2$ ,

Then $dfrac{du}{dx}=2dfrac{dy}{dx}dfrac{d^2y}{dx^2}$



$2dfrac{d^3y}{dx^3}=dfrac{d}{dx}left(dfrac{du}{dy}right)=dfrac{d}{dy}left(dfrac{du}{dy}right)dfrac{dy}{dx}=pmsqrt udfrac{d^2u}{dy^2}$

$thereforedfrac{du}{dy}pmsqrt udfrac{d^2u}{dy^2}sin y=0$

Answered by doraemonpaul on November 16, 2020

Add your own answers!

Ask a Question

Get help from others!

© 2024 All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP