What is the solution for (dy)/(dx)=x^2+12xy ?

The solution for (dy)/(dx)=x^2+12xy is y=e^{6x^2}*integral of e^{-6x^2}x^2

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(dy)/(dx)=x^2+12xy

\frac{d y}{d x} = x^{2} + 12 x y

y = e^{6 x^{2}} \cdot \int e^{- 6 x^{2}} x^{2} d x

Solution steps

\frac{d y}{d x} = x^{2} + 12 x y

Solve linear ODE:

y = e^{6 x^{2}} \cdot \int e^{- 6 x^{2}} x^{2} d x

y = e^{6 x^{2}} \cdot \int e^{- 6 x^{2}} x^{2} d x

What is the solution for (dy)/(dx)=x^2+12xy ?
The solution for (dy)/(dx)=x^2+12xy is y=e^{6x^2}*integral of e^{-6x^2}x^2