What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2 ?

The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2 is y=c_{1}e^{2x}+c_{2}e^x+(x^2)/2+(3x)/2+7/4

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(d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2

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

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{3 x}{2} + \frac{7}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{3 x}{2} + \frac{7}{4}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{x ^{2}}{2} + \frac{3 x}{2} + \frac{7}{4}

What is the solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2 ?
The solution for (d^2y)/(dx^2)-3(dy)/(dx)+2y=x^2 is y=c_{1}e^{2x}+c_{2}e^x+(x^2)/2+(3x)/2+7/4