What is the solution for y^{''}+y=sin(t),y(0)=9,y^'(0)=1 ?

The solution for y^{''}+y=sin(t),y(0)=9,y^'(0)=1 is y=9cos(t)+3/2 sin(t)-(tcos(t))/2

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y^{''}+y=sin(t),y(0)=9,y^'(0)=1

y^{^{''}} + y = sin (t), y (0) = 9, y^{^{'}} (0) = 1

y = 9 cos (t) + \frac{3}{2} sin (t) - \frac{t cos ( t )}{2}

Solution steps

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

Solve linear ODE:

y = 9 cos (t) + \frac{3}{2} sin (t) - \frac{t cos ( t )}{2}

y = 9 cos (t) + \frac{3}{2} sin (t) - \frac{t cos ( t )}{2}

What is the solution for y^{''}+y=sin(t),y(0)=9,y^'(0)=1 ?
The solution for y^{''}+y=sin(t),y(0)=9,y^'(0)=1 is y=9cos(t)+3/2 sin(t)-(tcos(t))/2