Need help with simplification of the DE

Nov 2015
246
4
hyderabad
Hi all,

I couldn't simplify exactly to get the correct answers(more then 1) for the attached multiple answers question.

Attaching the steps done at my end as well.

Thanks a lot in advance :)
 

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skeeter

Math Team
Jul 2011
3,356
1,848
Texas
$y^{-1/3} \, dy = 2\sin{x}\cos{x} \, dx$

$\dfrac{3}{2} y^{2/3} = \sin^2{x} + C$

$y(0) = 0 \implies C = 0$

$y^{2/3} = \dfrac{2}{3}\sin^2{x}$

$y = \left(\dfrac{2}{3}\sin^2{x} \right)^{3/2}$

$y = \sqrt{\dfrac{8}{27}} \sin^3{x}$

there's one ... is there another ?
 
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SDK

Sep 2016
804
544
USA
There is no reason to try to solve the DE. You have multiple choices so just plug each into the ODE and check whether it’s satisfied. I strongly suspect this is what you are expected to do here.
 
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Nov 2015
246
4
hyderabad
Thanks a lot for the replies.
@Skeeter - thanks for simplifying it. There are 2 more answers given, options A,B & C. As SDK suggested, it works with substitution in this question.

I'm clear with the question now, thank you all :)