What is the solution for (xdy)/(dx)=-y+2x^2y,y(1)=1 ?

The solution for (xdy)/(dx)=-y+2x^2y,y(1)=1 is y=(e^{x^2+c_{1}})/x

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(xdy)/(dx)=-y+2x^2y,y(1)=1

\frac{x d y}{d x} = - y + 2 x^{2} y, y (1) = 1

y = \frac{e ^{x^{2} + c_{1}}}{x}

Solution steps

\frac{x d y}{d x} = - y + 2 x^{2} y

Solve separable ODE:

y = \frac{e ^{x^{2} + c_{1}}}{x}

y = \frac{e ^{x^{2} + c_{1}}}{x}

\frac{d}{d x} (9 x - 8 x)

y \to 2 lim (4 y^{2} - 2 y)

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What is the solution for (xdy)/(dx)=-y+2x^2y,y(1)=1 ?
The solution for (xdy)/(dx)=-y+2x^2y,y(1)=1 is y=(e^{x^2+c_{1}})/x