What is the solution for x*(dy)/(dx)=-y+2x^2y ?

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

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x*(dy)/(dx)=-y+2x^2y

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

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

Solution steps

x \cdot \frac{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{\partial}{\partial y} (x^{2} + 2 y^{2} - 1)

\int \frac{9 x ^{8} + 8}{x ^{9} + 8 x} d x

\frac{\partial}{\partial x} (2 x e^{x^{2} + y^{2}})

8 y^{^{''}} + 32 y^{^{'}} = 0, y (2) = 1, y^{^{'}} (- 1) = 1

\frac{x ^{2}}{2 + x}

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