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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = 3 x^{2} y^{2}

\frac{d y}{d t} = \frac{t}{y - t ^{2} y}, y (0) = 4

x \frac{d y}{d x} = e^{6 y + x}, x > 0

\frac{d N}{d t} = k N (t)

\frac{d v}{d t} + 2 v = 32

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