Question

Solve xdy/dx - 2y = x²

Answer 1

We have, x=dydx+2y=x2

⇒dydx+2xy=x

The above equation is a linear differential equation in y.

∴IF=e∫2xdx=e2logx=x2

Hence, required solution will be

y.x2=∫x.x2dx+C1

⇒yx2=x44+C1

⇒yx2=x4+4C14

⇒y=x4+C4x2

NOT COPIED ORIGINAL ANSWER

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