What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=5x ?

The solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=5x is y=c_{1}e^{5x}+c_{2}e^{-x}-x+4/5

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(d^2y)/(dx^2)-4(dy)/(dx)-5y=5x

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 5 y = 5 x

y = c_{1} e^{5 x} + c_{2} e^{- x} - x + \frac{4}{5}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 \frac{d y}{d x} - 5 y = 5 x

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- x} - x + \frac{4}{5}

y = c_{1} e^{5 x} + c_{2} e^{- x} - x + \frac{4}{5}

2 y^{^{''}} + 50 y = 2 cos^{2} (5 x)

y^{^{''}} - y^{^{'}} - \frac{3}{4} y = cos (2 t)

y^{^{''}} + 2 y^{^{'}} + 5 y = e^{(- x)} sin (2 x)

y^{^{'''}} - 4 y^{^{'}} = x e^{2 x}

y^{^{''}} + y^{^{'}} - 2 y = 3 e^{- 2 t}

What is the solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=5x ?
The solution for (d^2y)/(dx^2)-4(dy)/(dx)-5y=5x is y=c_{1}e^{5x}+c_{2}e^{-x}-x+4/5