What is the solution for x^{''}+2x^'+2x=0,x(0)=1,x^'(0)=0 ?

The solution for x^{''}+2x^'+2x=0,x(0)=1,x^'(0)=0 is x=e^{-t}(cos(t)+sin(t))

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x^{''}+2x^'+2x=0,x(0)=1,x^'(0)=0

x^{^{''}} + 2 x^{^{'}} + 2 x = 0, x (0) = 1, x^{^{'}} (0) = 0

x = e^{- t} (cos (t) + sin (t))

Solution steps

x^{''} (t) + 2 x^{'} (t) + 2 x = 0

Solve linear ODE:

x = e^{- t} (cos (t) + sin (t))

x = e^{- t} (cos (t) + sin (t))

What is the solution for x^{''}+2x^'+2x=0,x(0)=1,x^'(0)=0 ?
The solution for x^{''}+2x^'+2x=0,x(0)=1,x^'(0)=0 is x=e^{-t}(cos(t)+sin(t))