What is the solution for y^{''}+y=2,y(0)=0 ?

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

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y^{''}+y=2,y(0)=0

y^{^{''}} + y = 2, y (0) = 0

y = - 2 cos (t) + c_{2} sin (t) + 2

Solution steps

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

Solve linear ODE:

y = - 2 cos (t) + c_{2} sin (t) + 2

y = - 2 cos (t) + c_{2} sin (t) + 2

y^{^{''}} + 5 y^{^{'}} - 24 y = - 92 t + 48 t^{2}

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

y^{^{''}} - 5 y^{^{'}} + 4 y = e^{4 t}

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

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

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