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

The solution for y^{''}+y=3cos(t),y(0)=0,y^'(0)=0 is y=(3tsin(t))/2

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

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

y = \frac{3 t sin ( t )}{2}

Solution steps

y^{''} (t) + y = 3 cos (t)

Solve linear ODE:

y = \frac{3 t sin ( t )}{2}

y = \frac{3 t sin ( t )}{2}

What is the solution for y^{''}+y=3cos(t),y(0)=0,y^'(0)=0 ?
The solution for y^{''}+y=3cos(t),y(0)=0,y^'(0)=0 is y=(3tsin(t))/2