What is the solution for y^{''}+16y=64t,y(0)=3,y^'(0)=2 ?

The solution for y^{''}+16y=64t,y(0)=3,y^'(0)=2 is y=3cos(4t)-1/2 sin(4t)+4t

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y^{''}+16y=64t,y(0)=3,y^'(0)=2

y^{^{''}} + 16 y = 64 t, y (0) = 3, y^{^{'}} (0) = 2

y = 3 cos (4 t) - \frac{1}{2} sin (4 t) + 4 t

Solution steps

y^{''} (t) + 16 y = 64 t

Solve linear ODE:

y = 3 cos (4 t) - \frac{1}{2} sin (4 t) + 4 t

y = 3 cos (4 t) - \frac{1}{2} sin (4 t) + 4 t

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{- 4 t}, y^{^{'}} (0) = 0, y (0) = 1

y^{^{''}} + 4 y = 4 t^{2} - 4 t + 10

2 y^{^{''}} - 5 y^{^{'}} + 3 y = (14 x - 10) e^{3 x}

y^{^{''}} + 9 y = 12 cos (3 t), y (0) = - 1, y^{^{'}} (0) = 1

4 x^{^{''}} + 324 x = 8 sin (t)

What is the solution for y^{''}+16y=64t,y(0)=3,y^'(0)=2 ?
The solution for y^{''}+16y=64t,y(0)=3,y^'(0)=2 is y=3cos(4t)-1/2 sin(4t)+4t