What is the solution for y^{''}+4y=g(t),y(0)=5,y^'(0)=16 ?

The solution for y^{''}+4y=g(t),y(0)=5,y^'(0)=16 is y=5cos(2t)+(sin(2t)(64-g))/8+(gt)/4

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y^{''}+4y=g(t),y(0)=5,y^'(0)=16

y^{^{''}} + 4 y = g (t), y (0) = 5, y^{^{'}} (0) = 16

y = 5 cos (2 t) + \frac{sin ( 2 t ) ( 64 - g )}{8} + \frac{g t}{4}

Solution steps

y^{''} (t) + 4 y = g (t)

Solve linear ODE:

y = 5 cos (2 t) + \frac{sin ( 2 t ) ( 64 - g )}{8} + \frac{g t}{4}

y = 5 cos (2 t) + \frac{sin ( 2 t ) ( 64 - g )}{8} + \frac{g t}{4}

x^{^{''}} - x = t

4 y^{^{''}} - 4 y^{^{'}} + y = 16 e^{\frac{1}{2} t}

16 y^{^{''''}} - y = e^{\frac{x}{2}}

y^{^{''}} + 5 y^{^{'}} + 6 y = 36 e^{t}, y (0) = - 5, y^{^{'}} (0) = 21

y^{^{''}} - 5 y^{^{'}} + 6 y = 2 x + 3 e^{8 x}

What is the solution for y^{''}+4y=g(t),y(0)=5,y^'(0)=16 ?
The solution for y^{''}+4y=g(t),y(0)=5,y^'(0)=16 is y=5cos(2t)+(sin(2t)(64-g))/8+(gt)/4