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?

Hint:

With reference to http://eqworld.ipmnet.ru/en/solutions/ode/ode0503.pdf,

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

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

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

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

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

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

Answered by doraemonpaul on November 16, 2020

Get help from others!

Recent Answers

- Jon Church on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- Peter Machado on Why fry rice before boiling?
- haakon.io on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?

Recent Questions

- How can I transform graph image into a tikzpicture LaTeX code?
- How Do I Get The Ifruit App Off Of Gta 5 / Grand Theft Auto 5
- Iv’e designed a space elevator using a series of lasers. do you know anybody i could submit the designs too that could manufacture the concept and put it to use
- Need help finding a book. Female OP protagonist, magic
- Why is the WWF pending games (“Your turn”) area replaced w/ a column of “Bonus & Reward”gift boxes?

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