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September 10th, 2019, 09:05 AM  #1 
Senior Member Joined: Nov 2015 From: hyderabad 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. Thanks a lot in advance 
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 ? 
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 itâ€™s satisfied. I strongly suspect this is what you are expected to do here.
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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