What is the solution for (dy}{dx}=\frac{y+x^2y)/x ?

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

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(dy}{dx}=\frac{y+x^2y)/x

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

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

Solution steps

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

Solve separable ODE:

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

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

x \frac{d y}{d x} - y = 2 x^{4} y, y (1) = 7

\frac{d y}{d x} y^{2} = ln (x)

y^{^{'}} = 1 - 0.4 y

y^{^{'}} = \frac{8 x ^{3} + 1}{3 y ^{2}}

\frac{d y}{d x} = - \frac{0.9}{cos ( y )}, y (0) = \frac{π}{3}

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