My Math Forum Need help with simplification of the DE

 Differential Equations Ordinary and Partial Differential Equations Math Forum

September 10th, 2019, 09:05 AM   #1
Senior Member

Joined: Nov 2015

Posts: 242
Thanks: 4

Need help with simplification of the DE

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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 September 10th, 2019, 09:49 AM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 3,016 Thanks: 1600 $y^{-1/3} \, dy = 2\sin{x}\cos{x} \, dx$ $\dfrac{3}{2} y^{2/3} = \sin^2{x} + C$ $y(0) = 0 \implies C = 0$ $y^{2/3} = \dfrac{2}{3}\sin^2{x}$ $y = \left(\dfrac{2}{3}\sin^2{x} \right)^{3/2}$ $y = \sqrt{\dfrac{8}{27}} \sin^3{x}$ there's one ... is there another ? Thanks from greg1313, topsquark and Lalitha183
 September 10th, 2019, 05:29 PM #3 Senior Member   Joined: Sep 2016 From: USA Posts: 645 Thanks: 408 Math Focus: Dynamical systems, analytic function theory, numerics 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. Thanks from topsquark and Lalitha183 Last edited by skipjack; September 10th, 2019 at 10:08 PM.
 September 10th, 2019, 06:45 PM #4 Senior Member   Joined: Nov 2015 From: hyderabad Posts: 242 Thanks: 4 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

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