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=5+3/16-3/16 e^{-16t}+9t

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

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

x = 5 + \frac{3}{16} - \frac{3}{16} e^{- 16 t} + 9 t

Solution steps

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

Solve linear ODE:

x = 5 + \frac{3}{16} - \frac{3}{16} e^{- 16 t} + 9 t

x = 5 + \frac{3}{16} - \frac{3}{16} e^{- 16 t} + 9 t

y^{^{''}} - 90 y = sin (2 x)

y^{^{''}} + 25 \cdot y = \frac{1}{sin ( 5 \cdot x )}

y^{^{''}} + y = 3 sin (2 x) + 5 x cos (2 x)

- 6 y^{^{''}} + 5 y^{^{'}} - 1 y = 1 t^{2} - 1 t + 6 e^{2} t

y^{^{''}} + 4 y^{^{'}} + 29 y = 200 sin (x)

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=5+3/16-3/16 e^{-16t}+9t