What is the solution for y^{''}+16y=g(t),y(0)=5,y^'(0)=0 ?

The solution for y^{''}+16y=g(t),y(0)=5,y^'(0)=0 is y=5cos(4t)-(gsin(4t))/(64)+(gt)/(16)

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y^{''}+16y=g(t),y(0)=5,y^'(0)=0

y^{^{''}} + 16 y = g (t), y (0) = 5, y^{^{'}} (0) = 0

y = 5 cos (4 t) - \frac{g sin ( 4 t )}{64} + \frac{g t}{16}

Solution steps

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

Solve linear ODE:

y = 5 cos (4 t) - \frac{g sin ( 4 t )}{64} + \frac{g t}{16}

y = 5 cos (4 t) - \frac{g sin ( 4 t )}{64} + \frac{g t}{16}

What is the solution for y^{''}+16y=g(t),y(0)=5,y^'(0)=0 ?
The solution for y^{''}+16y=g(t),y(0)=5,y^'(0)=0 is y=5cos(4t)-(gsin(4t))/(64)+(gt)/(16)