What is the solution for (d^2u)/(dx^2)-u=6 ?

The solution for (d^2u)/(dx^2)-u=6 is u=c_{1}e^x+c_{2}e^{-x}-6

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(d^2u)/(dx^2)-u=6

\frac{d ^{2} u}{d x ^{2}} - u = 6

u = c_{1} e^{x} + c_{2} e^{- x} - 6

Solution steps

\frac{d ^{2} u}{d x ^{2}} - u = 6

Solve linear ODE:

u = c_{1} e^{x} + c_{2} e^{- x} - 6

u = c_{1} e^{x} + c_{2} e^{- x} - 6

y^{^{'''}} - 6 y^{^{''}} + 11 y^{^{'}} - 6 y = e^{x}

y^{^{''}} - 4 y = - 7 e^{2 x} + x

y^{^{''}} - 2 y^{^{'}} + 5 y = 1 + t

y^{^{''}} + y^{^{'}} = cos (2 t)

y^{^{''}} + 16 y = 8 e^{4 t} + 8 sin (2 t)

What is the solution for (d^2u)/(dx^2)-u=6 ?
The solution for (d^2u)/(dx^2)-u=6 is u=c_{1}e^x+c_{2}e^{-x}-6