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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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