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

The solution for y^{''}+y=16cos(t),y(0)=0,y^'(0)=0 is y=8tsin(t)

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y^{''}+y=16cos(t),y(0)=0,y^'(0)=0

y^{^{''}} + y = 16 cos (t), y (0) = 0, y^{^{'}} (0) = 0

y = 8 t sin (t)

Solution steps

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

Solve linear ODE:

y = 8 t sin (t)

y = 8 t sin (t)

y^{^{''}} + 9 y = 2 x - 5

(D^{2} + 1) v = 1

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

x^{^{''}} + 16 x = 144, x (0) = 5, x^{^{'}} (0) = 12

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

What is the solution for y^{''}+y=16cos(t),y(0)=0,y^'(0)=0 ?
The solution for y^{''}+y=16cos(t),y(0)=0,y^'(0)=0 is y=8tsin(t)