What is the solution for y^{''}+10y^'+26y=0,y(0)=1,y^'(0)=0 ?

The solution for y^{''}+10y^'+26y=0,y(0)=1,y^'(0)=0 is y=e^{-5t}(cos(t)+5sin(t))

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y^{''}+10y^'+26y=0,y(0)=1,y^'(0)=0

y^{^{''}} + 10 y^{^{'}} + 26 y = 0, y (0) = 1, y^{^{'}} (0) = 0

y = e^{- 5 t} (cos (t) + 5 sin (t))

Solution steps

y^{''} (t) + 10 y^{'} (t) + 26 y = 0

Solve linear ODE:

y = e^{- 5 t} (cos (t) + 5 sin (t))

y = e^{- 5 t} (cos (t) + 5 sin (t))

\frac{d ^{2} y}{d x ^{2}} + a^{2} y = 0

x^{^{'''}} + 4 x^{^{''}} + 13 x^{^{'}} = 0

(d^{4} - 5 d^{3} + 5 d^{2} + 5 d - 6) y = 0

14 y^{^{''''}} + 95 y^{^{''}} + 144 y = 0

y^{^{''}} = 5 y

What is the solution for y^{''}+10y^'+26y=0,y(0)=1,y^'(0)=0 ?
The solution for y^{''}+10y^'+26y=0,y(0)=1,y^'(0)=0 is y=e^{-5t}(cos(t)+5sin(t))