What is the solution for 6y^{''}-y^'-7y=-7 ?

The solution for 6y^{''}-y^'-7y=-7 is y=c_{1}e^{(7t)/6}+c_{2}e^{-t}+1

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6y^{''}-y^'-7y=-7

6 y^{^{''}} - y^{^{'}} - 7 y = - 7

y = c_{1} e^{\frac{7 t}{6}} + c_{2} e^{- t} + 1

Solution steps

6 y^{''} (t) - y^{'} (t) - 7 y = - 7

Solve linear ODE:

y = c_{1} e^{\frac{7 t}{6}} + c_{2} e^{- t} + 1

y = c_{1} e^{\frac{7 t}{6}} + c_{2} e^{- t} + 1

y^{^{''}} - y^{^{'}} - 6 y = 58 cos (3 x)

y^{^{''}} - 9 y = (x^{2} - 7) sin (3 x)

y^{^{''}} + 36 y = csc^{2} (6 x)

y^{^{''}} + 6 y^{^{'}} - 40 y = 1 - 3 x + x^{2}

y^{^{''}} + 10 y^{^{'}} + 25 y = e^{2 x}, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for 6y^{''}-y^'-7y=-7 ?
The solution for 6y^{''}-y^'-7y=-7 is y=c_{1}e^{(7t)/6}+c_{2}e^{-t}+1