Solve differential equation x\frac{dy}{dx}-2y=x^3 \sin^2(x)

tabita57i

tabita57i

Answered question

2020-11-27

Solve differential equation xdydx2y=x3sin2(x)

Answer & Explanation

Lacey-May Snyder

Lacey-May Snyder

Skilled2020-11-28Added 88 answers

xdydx2y=x3sin2(x)
xdydx2x=x2sin(x)
I.F.=e2xdx
=e2lnx
=e{lnx2}
=x2
yx2=x2(x2sin2x)dx+c
=sin2xdx+c
=1cos2x2dx+c
=x2sin2x4+c
y=x32x2sin2x4+cx2
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-14Added 2605 answers

Answer is given below (on video)

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