What is the solution for y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1 ?

The solution for y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1 is y=5.325e^t-1.775e^{-t}-3.55cos(t)

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y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1

y^{^{''}} - y = 7.1 cos (t), y (0) = 0, y^{^{'}} (0) = 7.1

y = 5.325 e^{t} - 1.775 e^{- t} - 3.55 cos (t)

Solution steps

y^{''} (t) - y = 7.1 cos (t)

Solve linear ODE:

y = 5.325 e^{t} - 1.775 e^{- t} - 3.55 cos (t)

y = 5.325 e^{t} - 1.775 e^{- t} - 3.55 cos (t)

y^{^{''}} - 4 y^{^{'}} + 3 y = 8 e^{x}

y^{^{''}} + 3 y = t^{3}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{'''}} + 2 y^{^{'}} - y^{^{'}} - 2 y = sin (3 t)

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

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

What is the solution for y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1 ?
The solution for y^{''}-y=7.1cos(t),y(0)=0,y^'(0)=7.1 is y=5.325e^t-1.775e^{-t}-3.55cos(t)