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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 4 y = (x + 1) e^{(2 x)}

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

y^{^{''}} - a^{2} y = - 2 sin (π \cdot x) - 4 sin (3 \cdot π \cdot x)

(d - 2) y = e^{2} x

y^{^{''}} + \frac{7}{2} y^{^{'}} + \frac{3}{2} y = 2 e^{- 3 x}

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