What is the solution for y^{''}-3y^'+2y=e^{3x}+x^2 ?

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

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y^{''}-3y^'+2y=e^{3x}+x^2

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3 x} + x^{2}

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

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = e^{3 x} + x^{2}

Solve linear ODE:

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

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

x \to 0 lim (x^{2} - 2)

\frac{3}{x ^{2} - x - 2}, 1

\frac{\partial}{\partial y} (4 - x^{2} - 6 y^{2})

(8 t + y + 2) d t - d y = 0

\frac{csc ( x )}{1 + csc ( x )}

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