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

The solution for (dy)/(dx)-2y+x^2=0 is y=(x^2)/2+x/2+1/4+c_{1}e^{2x}

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(dy)/(dx)-2y+x^2=0

\frac{d y}{d x} - 2 y + x^{2} = 0

y = \frac{x ^{2}}{2} + \frac{x}{2} + \frac{1}{4} + c_{1} e^{2 x}

Solution steps

\frac{d y}{d x} - 2 y + x^{2} = 0

Solve linear ODE:

y = \frac{x ^{2}}{2} + \frac{x}{2} + \frac{1}{4} + c_{1} e^{2 x}

y = \frac{x ^{2}}{2} + \frac{x}{2} + \frac{1}{4} + c_{1} e^{2 x}

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f (x) = 3 x^{4} - 12 x^{3} + 4

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What is the solution for (dy)/(dx)-2y+x^2=0 ?
The solution for (dy)/(dx)-2y+x^2=0 is y=(x^2)/2+x/2+1/4+c_{1}e^{2x}