What is the solution for x^{''}+6x^'+34x=68,x(0)=5,x^'(0)=7 ?

The solution for x^{''}+6x^'+34x=68,x(0)=5,x^'(0)=7 is x=e^{-3t}(3cos(5t)+16/5 sin(5t))+2

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x^{''}+6x^'+34x=68,x(0)=5,x^'(0)=7

x^{^{''}} + 6 x^{^{'}} + 34 x = 68, x (0) = 5, x^{^{'}} (0) = 7

x = e^{- 3 t} (3 cos (5 t) + \frac{16}{5} sin (5 t)) + 2

Solution steps

x^{''} (t) + 6 x^{'} (t) + 34 x = 68

Solve linear ODE:

x = e^{- 3 t} (3 cos (5 t) + \frac{16}{5} sin (5 t)) + 2

x = e^{- 3 t} (3 cos (5 t) + \frac{16}{5} sin (5 t)) + 2

What is the solution for x^{''}+6x^'+34x=68,x(0)=5,x^'(0)=7 ?
The solution for x^{''}+6x^'+34x=68,x(0)=5,x^'(0)=7 is x=e^{-3t}(3cos(5t)+16/5 sin(5t))+2