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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = (y + 2 t)^{2}

- 2 y - y^{2} d x + (3 + 2 x - x^{2}) d y = 0

y^{^{''}} - y^{^{'}} - 2 y = cos (x) - sin (2 x)

\frac{d}{d x} (- 2 a sin (2 x) + 2 b cos (2 x))

y = 2 + 8 e^{6 x}

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