What is the solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=7e^{8x} ?

The solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=7e^{8x} is y=c_{1}e^{8x}+c_{2}xe^{8x}+(7e^{8x}x^2)/2

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(d^2y)/(dx^2)-16(dy)/(dx)+64y=7e^{8x}

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 7 e^{8 x}

y = c_{1} e^{8 x} + c_{2} x e^{8 x} + \frac{7 e ^{8 x} x ^{2}}{2}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 64 y = 7 e^{8 x}

Solve linear ODE:

y = c_{1} e^{8 x} + c_{2} x e^{8 x} + \frac{7 e ^{8 x} x ^{2}}{2}

y = c_{1} e^{8 x} + c_{2} x e^{8 x} + \frac{7 e ^{8 x} x ^{2}}{2}

y^{^{''}} + 36 y = cos (8 x)

y^{^{'''}} + y^{^{'}} = ln (x)

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

y^{^{''}} + y = sin (t) cos (t)

y^{^{''}} + 6 y^{^{'}} + 9 y = \frac{( 2 e ^{- 3 x} )}{x ^{2} + 1}

What is the solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=7e^{8x} ?
The solution for (d^2y)/(dx^2)-16(dy)/(dx)+64y=7e^{8x} is y=c_{1}e^{8x}+c_{2}xe^{8x}+(7e^{8x}x^2)/2