What is the solution for 0.5y^{''}+y^'+10y=0,y(0)=0,y^'(0)=1 ?

The solution for 0.5y^{''}+y^'+10y=0,y(0)=0,y^'(0)=1 is y= 1/(sqrt(19))e^{-t}sin(sqrt(19)t)

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0.5y^{''}+y^'+10y=0,y(0)=0,y^'(0)=1

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

y = \frac{1}{19} e^{- t} sin (19 t)

Solution steps

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

Solve linear ODE:

y = \frac{1}{19} e^{- t} sin (19 t)

y = \frac{1}{19} e^{- t} sin (19 t)

y^{^{''}} + \frac{a}{4} y = 0, y^{^{'}} (π) = 0, y^{^{'}} (0) = 0

x^{^{''}} + 2 x^{^{'}} + 10 x = 0, x (0) = 1, x^{^{'}} (0) = 0

4 y^{^{''}} + \frac{16}{0.25} y = 0, y (0) = 0, y^{^{'}} (0) = 0

\frac{16}{32} x^{^{''}} + x^{^{'}} + 2 x = 0, x (0) = - 2, x^{^{'}} (0) = 1

100 y^{^{'''}} + 60 y^{^{''}} + 9 y^{^{'}} = 0

What is the solution for 0.5y^{''}+y^'+10y=0,y(0)=0,y^'(0)=1 ?
The solution for 0.5y^{''}+y^'+10y=0,y(0)=0,y^'(0)=1 is y= 1/(sqrt(19))e^{-t}sin(sqrt(19)t)