What is the solution for (dy)/(dx)+x^2y=3x^2 ?

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

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(dy)/(dx)+x^2y=3x^2

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

y = e^{- \frac{x ^{3}}{3} + c_{1}} + 3

Solution steps

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

Solve separable ODE:

y = e^{- \frac{x ^{3}}{3} + c_{1}} + 3

y = e^{- \frac{x ^{3}}{3} + c_{1}} + 3

y^{^{'}} = e^{y} sin (t)

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

\frac{d y}{d x} y = \frac{sin ( x )}{x ^{3}}

y^{^{'}} = \frac{ln ( x )}{x y}

\frac{d y}{d x} = - \frac{1}{sin ( y )}, y (- 3) = \frac{π}{2}

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