# Need help with simplification of the DE

#### Lalitha183

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.

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#### skeeter

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

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

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

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

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

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

there's one ... is there another ?

3 people

#### SDK

There is no reason to try to solve the DE. You have multiple choices so just plug each into the ODE and check whether itâ€™s satisfied. I strongly suspect this is what you are expected to do here.

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2 people

#### Lalitha183

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