What is the solution for y^{''}-2y^'+y=11e^x ?

The solution for y^{''}-2y^'+y=11e^x is y=c_{1}e^x+c_{2}xe^x+(11e^xx^2)/2

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y^{''}-2y^'+y=11e^x

y^{^{''}} - 2 y^{^{'}} + y = 11 e^{x}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{11 e ^{x} x ^{2}}{2}

Solution steps

y^{''} (x) - 2 y^{'} (x) + y = 11 e^{x}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{11 e ^{x} x ^{2}}{2}

y = c_{1} e^{x} + c_{2} x e^{x} + \frac{11 e ^{x} x ^{2}}{2}

y^{^{''}} + 36 y = 13 sec^{2} (6 t)

y^{^{''}} + 4 y = 9 t, y^{^{'}} (0) = 7

y^{^{''}} + 3 y^{^{'}} - 4 y = 2 cos (3 x)

y^{^{''}} + 2 y^{^{'}} + y = t^{2} - 6

y^{^{''}} + 2 y^{^{'}} + 2 y = \frac{e ^{- x}}{cos ( x )}

What is the solution for y^{''}-2y^'+y=11e^x ?
The solution for y^{''}-2y^'+y=11e^x is y=c_{1}e^x+c_{2}xe^x+(11e^xx^2)/2