What is the solution for (dy)/(dx)+2xy=2x^3,y(0)=2 ?

The solution for (dy)/(dx)+2xy=2x^3,y(0)=2 is y=x^2-1+3/(e^{x^2)}

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(dy)/(dx)+2xy=2x^3,y(0)=2

\frac{d y}{d x} + 2 x y = 2 x^{3}, y (0) = 2

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

Solution steps

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

Solve linear ODE:

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

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

\int 1 d ln (x) d x

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

y = ln (t^{2}) - arctan (\frac{t}{3})

\frac{t + 1710}{50 ( t + 2 )}

- \frac{2}{s ^{3} ( s - 3 )}

What is the solution for (dy)/(dx)+2xy=2x^3,y(0)=2 ?
The solution for (dy)/(dx)+2xy=2x^3,y(0)=2 is y=x^2-1+3/(e^{x^2)}