What is the solution for y^{''}-3y^'-4y=-16t,y(0)=-4,y^'(0)=-5 ?

The solution for y^{''}-3y^'-4y=-16t,y(0)=-4,y^'(0)=-5 is y=-2e^{4t}+e^{-t}+4t-3

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y^{''}-3y^'-4y=-16t,y(0)=-4,y^'(0)=-5

y^{^{''}} - 3 y^{^{'}} - 4 y = - 16 t, y (0) = - 4, y^{^{'}} (0) = - 5

y = - 2 e^{4 t} + e^{- t} + 4 t - 3

Solution steps

y^{''} (t) - 3 y^{'} (t) - 4 y = - 16 t

Solve linear ODE:

y = - 2 e^{4 t} + e^{- t} + 4 t - 3

y = - 2 e^{4 t} + e^{- t} + 4 t - 3

y^{^{''}} + 4 y = 5 sin (2 x) - 7 cos (2 x)

y^{^{''}} - 4 y^{^{'}} = 6 e^{3 x} - 3 e^{- x}

2 y^{^{''}} + 8 y^{^{'}} - y = 16

y^{^{'''}} + 4 y^{^{'}} = tan (2 x)

y^{^{''}} + y^{^{'}} = e^{5 x}

What is the solution for y^{''}-3y^'-4y=-16t,y(0)=-4,y^'(0)=-5 ?
The solution for y^{''}-3y^'-4y=-16t,y(0)=-4,y^'(0)=-5 is y=-2e^{4t}+e^{-t}+4t-3