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

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

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

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

y = e^{- x^{2}} + 1

Solution steps

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

Solve separable ODE:

y = e^{- x^{2}} + 1

y = e^{- x^{2}} + 1

\frac{d y}{d x} + 5 y = 20, y (0) = 2

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

y^{^{'}} = x^{2} - 2 x^{2} y

1 - y^{2} (d x) - 1 + x^{2} (d y) = 0

1 = \frac{5}{3} y + \frac{d y}{d x}

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