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

The solution for (dy)/(dx)+2y=x^2+2x is y=(x^2)/2+x/2-1/4+(c_{1})/(e^{2x)}

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

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

y = \frac{x ^{2}}{2} + \frac{x}{2} - \frac{1}{4} + \frac{c _{1}}{e ^{2 x}}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{2}}{2} + \frac{x}{2} - \frac{1}{4} + \frac{c _{1}}{e ^{2 x}}

y = \frac{x ^{2}}{2} + \frac{x}{2} - \frac{1}{4} + \frac{c _{1}}{e ^{2 x}}

\int \frac{13 x ^{2}}{x ^{2} - 4} d x

f (x) = \frac{3}{2 x ^{2}}

\frac{d}{d x} (\frac{1}{x ^{2} - 9})

\int cos^{2} (9 x) d x

\frac{\partial}{\partial x} (y e^{- x})

What is the solution for (dy)/(dx)+2y=x^2+2x ?
The solution for (dy)/(dx)+2y=x^2+2x is y=(x^2)/2+x/2-1/4+(c_{1})/(e^{2x)}