What is the solution for (dy)/(dx)+3x^2y=5x^2 ?

The solution for (dy)/(dx)+3x^2y=5x^2 is y=(e^{-x^3+c_{1}})/3+5/3

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(dy)/(dx)+3x^2y=5x^2

\frac{d y}{d x} + 3 x^{2} y = 5 x^{2}

y = \frac{e ^{- x^{3} + c_{1}}}{3} + \frac{5}{3}

Solution steps

\frac{d y}{d x} + 3 x^{2} y = 5 x^{2}

Solve separable ODE:

y = \frac{e ^{- x^{3} + c_{1}}}{3} + \frac{5}{3}

y = \frac{e ^{- x^{3} + c_{1}}}{3} + \frac{5}{3}

\frac{d y}{d x} = \frac{1}{3} y cos^{2} (y)

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

x - 1 \frac{d y}{d x} = \frac{x}{y}

\frac{d y}{d x} = \frac{y - 1}{x + 3}

e^{2 x - y} d x + e^{y - 2 x} d y = 0

What is the solution for (dy)/(dx)+3x^2y=5x^2 ?
The solution for (dy)/(dx)+3x^2y=5x^2 is y=(e^{-x^3+c_{1}})/3+5/3