What is the solution for x^{''}+16x=144,x(0)=5,x^'(0)=12 ?

The solution for x^{''}+16x=144,x(0)=5,x^'(0)=12 is x=-4cos(4t)+3sin(4t)+9

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

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

x = - 4 cos (4 t) + 3 sin (4 t) + 9

Solution steps

x^{''} (t) + 16 x = 144

Solve linear ODE:

x = - 4 cos (4 t) + 3 sin (4 t) + 9

x = - 4 cos (4 t) + 3 sin (4 t) + 9

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

x^{^{''}} + 6 x^{^{'}} + 9 = 0

y^{^{''}} + 4 y = 3, y^{^{'}} (0) = 0, y (0) = 0

y^{^{''}} - \frac{7}{4} y^{^{'}} + \frac{3}{4} y = t e^{2 t} sin (- 2 t)

x^{^{''}} - x = - 4 e^{- t}

What is the solution for x^{''}+16x=144,x(0)=5,x^'(0)=12 ?
The solution for x^{''}+16x=144,x(0)=5,x^'(0)=12 is x=-4cos(4t)+3sin(4t)+9