What is the solution for (d^2y)/(dx^2)-8(dy)/(dx)+16y=e^{4x} ?

The solution for (d^2y)/(dx^2)-8(dy)/(dx)+16y=e^{4x} is y=c_{1}e^{4x}+c_{2}xe^{4x}+(e^{4x}x^2)/2

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(d^2y)/(dx^2)-8(dy)/(dx)+16y=e^{4x}

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 16 y = e^{4 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 8 \frac{d y}{d x} + 16 y = e^{4 x}

Solve linear ODE:

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

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

y^{^{''}} + y = 5 x sin (x)

y^{^{''}} - 4 y = x e^{x}

y^{^{''}} - y^{^{'}} - 2 y = cosh (2 t)

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

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

What is the solution for (d^2y)/(dx^2)-8(dy)/(dx)+16y=e^{4x} ?
The solution for (d^2y)/(dx^2)-8(dy)/(dx)+16y=e^{4x} is y=c_{1}e^{4x}+c_{2}xe^{4x}+(e^{4x}x^2)/2