What is the solution for y^{''}-3y^'-10y=54e^{7t},y(0)=5 ?

The solution for y^{''}-3y^'-10y=54e^{7t},y(0)=5 is y=(-c_{2}+2)e^{5t}+c_{2}e^{-2t}+3e^{7t}

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y^{''}-3y^'-10y=54e^{7t},y(0)=5

y^{^{''}} - 3 y^{^{'}} - 10 y = 54 e^{7 t}, y (0) = 5

y = (- c_{2} + 2) e^{5 t} + c_{2} e^{- 2 t} + 3 e^{7 t}

Solution steps

y^{''} (t) - 3 y^{'} (t) - 10 y = 54 e^{7 t}

Solve linear ODE:

y = (- c_{2} + 2) e^{5 t} + c_{2} e^{- 2 t} + 3 e^{7 t}

y = (- c_{2} + 2) e^{5 t} + c_{2} e^{- 2 t} + 3 e^{7 t}

y^{^{''}} + 9 y = - 2 e^{3} t

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

y^{^{''}} - 9 y = e^{(- 2 x)} (- 17 + 10 x)

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

y^{^{''}} + 5 y = - 9.81

What is the solution for y^{''}-3y^'-10y=54e^{7t},y(0)=5 ?
The solution for y^{''}-3y^'-10y=54e^{7t},y(0)=5 is y=(-c_{2}+2)e^{5t}+c_{2}e^{-2t}+3e^{7t}