What is the solution for (dy)/(dx)=2xy+3x^2e^{x^2} ?

The solution for (dy)/(dx)=2xy+3x^2e^{x^2} is y=e^{x^2}x^3+c_{1}e^{x^2}

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(dy)/(dx)=2xy+3x^2e^{x^2}

\frac{d y}{d x} = 2 x y + 3 x^{2} e^{x^{2}}

y = e^{x^{2}} x^{3} + c_{1} e^{x^{2}}

Solution steps

\frac{d y}{d x} = 2 x y + 3 x^{2} e^{x^{2}}

Solve linear ODE:

y = e^{x^{2}} x^{3} + c_{1} e^{x^{2}}

y = e^{x^{2}} x^{3} + c_{1} e^{x^{2}}

What is the solution for (dy)/(dx)=2xy+3x^2e^{x^2} ?
The solution for (dy)/(dx)=2xy+3x^2e^{x^2} is y=e^{x^2}x^3+c_{1}e^{x^2}