What is the solution for (D^2-10D+25)y=e^{5x} ?

The solution for (D^2-10D+25)y=e^{5x} is y=c_{1}e^{5x}+c_{2}xe^{5x}+(e^{5x}x^2)/2

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(D^2-10D+25)y=e^{5x}

(D^{2} - 10 D + 25) y = e^{5 x}

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{e ^{5 x} x ^{2}}{2}

Solution steps

(D^{2} - 10 D + 25) y = e^{5 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{e ^{5 x} x ^{2}}{2}

y = c_{1} e^{5 x} + c_{2} x e^{5 x} + \frac{e ^{5 x} x ^{2}}{2}

9 \frac{d ^{2} y}{d x ^{2}} + 3 y = 9 (x + 5), y (0) = 5

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

y^{^{''}} + 7 y^{^{'}} + 6 y = e^{2 x}

y^{^{''}} + 2 y^{^{'}} + 0.75 x = 0

y^{^{''}} + 6 y^{^{'}} + 10 y = 3 x - 3

What is the solution for (D^2-10D+25)y=e^{5x} ?
The solution for (D^2-10D+25)y=e^{5x} is y=c_{1}e^{5x}+c_{2}xe^{5x}+(e^{5x}x^2)/2