What is the solution for y^{''}+4y=16t,y(0)=3,y^'(0)=-6 ?

The solution for y^{''}+4y=16t,y(0)=3,y^'(0)=-6 is y=3cos(2t)-5sin(2t)+4t

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y^{''}+4y=16t,y(0)=3,y^'(0)=-6

y^{^{''}} + 4 y = 16 t, y (0) = 3, y^{^{'}} (0) = - 6

y = 3 cos (2 t) - 5 sin (2 t) + 4 t

Solution steps

y^{''} (t) + 4 y = 16 t

Solve linear ODE:

y = 3 cos (2 t) - 5 sin (2 t) + 4 t

y = 3 cos (2 t) - 5 sin (2 t) + 4 t

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

y^{^{''}} - 3 y^{^{'}} + 2 y = 9 e^{3 x}

y^{^{''}} - 2 y^{^{'}} + y = x^{\frac{- 1}{3}} e^{x}

y^{^{''}} + 4 y = t^{2} + 6 e^{t}

y^{^{''}} - 2 y^{^{'}} + 5 y = 10 x^{2} - 3 x - 3

What is the solution for y^{''}+4y=16t,y(0)=3,y^'(0)=-6 ?
The solution for y^{''}+4y=16t,y(0)=3,y^'(0)=-6 is y=3cos(2t)-5sin(2t)+4t