What is the solution for y^{''}-5y^'-6y=10 ?

The solution for y^{''}-5y^'-6y=10 is y=c_{1}e^{6t}+c_{2}e^{-t}-5/3

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y^{''}-5y^'-6y=10

y^{^{''}} - 5 y^{^{'}} - 6 y = 10

y = c_{1} e^{6 t} + c_{2} e^{- t} - \frac{5}{3}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 6 y = 10

Solve linear ODE:

y = c_{1} e^{6 t} + c_{2} e^{- t} - \frac{5}{3}

y = c_{1} e^{6 t} + c_{2} e^{- t} - \frac{5}{3}

3 \frac{d ^{2} y}{d x ^{2}} + 20 \frac{d y}{d x} + 25 y = cos (2 x)

y^{^{'''}} + 3 y^{^{'}} - 2 x = 0

(D^{2} + 4 D + 5) y = e^{(- x)} + 15 x

y^{^{''}} + y = 2 cos (x), y^{^{'}} (π) = 0, y (0) = 0

(D^{2} + 1) y = cos^{2} (x)

What is the solution for y^{''}-5y^'-6y=10 ?
The solution for y^{''}-5y^'-6y=10 is y=c_{1}e^{6t}+c_{2}e^{-t}-5/3