What is the solution for y^{''}+y^'=2sin(t),y(0)=0,y^'(0)=-4 ?

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

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y^{''}+y^'=2sin(t),y(0)=0,y^'(0)=-4

y^{^{''}} + y^{^{'}} = 2 sin (t), y (0) = 0, y^{^{'}} (0) = - 4

y = 3 e^{- t} - cos (t) - sin (t) - 2

Solution steps

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

Solve linear ODE:

y = 3 e^{- t} - cos (t) - sin (t) - 2

y = 3 e^{- t} - cos (t) - sin (t) - 2

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