What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+10y=e^{2x}+20 ?

The solution for (d^2y)/(dx^2)-7(dy)/(dx)+10y=e^{2x}+20 is y=c_{1}e^{5x}+c_{2}e^{2x}-(e^{2x}x)/3+2

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(d^2y)/(dx^2)-7(dy)/(dx)+10y=e^{2x}+20

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 10 y = e^{2 x} + 20

y = c_{1} e^{5 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x}{3} + 2

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 7 \frac{d y}{d x} + 10 y = e^{2 x} + 20

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x}{3} + 2

y = c_{1} e^{5 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x}{3} + 2

y^{^{''}} - 2 y^{^{'}} - 35 y = - 97 t + 70 t^{2}

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

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

y^{^{''}} + 9 y = sin (x) - 2

y^{^{'''}} - y^{^{'}} = tan (x)

What is the solution for (d^2y)/(dx^2)-7(dy)/(dx)+10y=e^{2x}+20 ?
The solution for (d^2y)/(dx^2)-7(dy)/(dx)+10y=e^{2x}+20 is y=c_{1}e^{5x}+c_{2}e^{2x}-(e^{2x}x)/3+2