What is the solution for y^{''}+y=5t^2-9,y(0)=0,y^'(0)=-2 ?

The solution for y^{''}+y=5t^2-9,y(0)=0,y^'(0)=-2 is y=19cos(t)-2sin(t)+5t^2-19

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y^{''}+y=5t^2-9,y(0)=0,y^'(0)=-2

y^{^{''}} + y = 5 t^{2} - 9, y (0) = 0, y^{^{'}} (0) = - 2

y = 19 cos (t) - 2 sin (t) + 5 t^{2} - 19

Solution steps

y^{''} (t) + y = 5 t^{2} - 9

Solve linear ODE:

y = 19 cos (t) - 2 sin (t) + 5 t^{2} - 19

y = 19 cos (t) - 2 sin (t) + 5 t^{2} - 19

What is the solution for y^{''}+y=5t^2-9,y(0)=0,y^'(0)=-2 ?
The solution for y^{''}+y=5t^2-9,y(0)=0,y^'(0)=-2 is y=19cos(t)-2sin(t)+5t^2-19