What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)-36y=e^{10x} ?

The solution for (d^2y)/(dx^2)-5(dy)/(dx)-36y=e^{10x} is y=c_{1}e^{9x}+c_{2}e^{-4x}+1/14 e^{10x}

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(d^2y)/(dx^2)-5(dy)/(dx)-36y=e^{10x}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 36 y = e^{10 x}

y = c_{1} e^{9 x} + c_{2} e^{- 4 x} + \frac{1}{14} e^{10 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} - 36 y = e^{10 x}

Solve linear ODE:

y = c_{1} e^{9 x} + c_{2} e^{- 4 x} + \frac{1}{14} e^{10 x}

y = c_{1} e^{9 x} + c_{2} e^{- 4 x} + \frac{1}{14} e^{10 x}

y^{^{''}} - 2 y^{^{'}} + 10 y = e x cos (3 x)

5 y^{^{''}} - 2 y^{^{'}} + 80 y = 24 sin (4 t)

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

x^{^{''}} + x^{^{'}} = e^{- t}

y^{^{''}} + 49 y = 8 cos (7 x) (3 x + 2)

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)-36y=e^{10x} ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)-36y=e^{10x} is y=c_{1}e^{9x}+c_{2}e^{-4x}+1/14 e^{10x}