What is the solution for y^{''}+1/2 y^'+1/16 y=0,y(0)=0,y^'(0)=5 ?

The solution for y^{''}+1/2 y^'+1/16 y=0,y(0)=0,y^'(0)=5 is y=5e^{-t/4}t

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y^{''}+1/2 y^'+1/16 y=0,y(0)=0,y^'(0)=5

y^{^{''}} + \frac{1}{2} y^{^{'}} + \frac{1}{16} y = 0, y (0) = 0, y^{^{'}} (0) = 5

y = 5 e^{- \frac{t}{4}} t

Solution steps

y^{''} (t) + \frac{1}{2} y^{'} (t) + \frac{1}{16} y = 0

Solve linear ODE:

y = 5 e^{- \frac{t}{4}} t

y = 5 e^{- \frac{t}{4}} t

\frac{\partial}{\partial y} (e^{x y} - z)

y^{^{''}} + 12 y^{^{'}} + 37 y = 0

x \to - 5 - lim (\frac{- 2}{x ^{2} - 25})

\int \frac{8}{64 - x ^{2}} d x

\frac{18 x + 4 x ^{2}}{( 9 + 4 x ) ^{2}}

What is the solution for y^{''}+1/2 y^'+1/16 y=0,y(0)=0,y^'(0)=5 ?
The solution for y^{''}+1/2 y^'+1/16 y=0,y(0)=0,y^'(0)=5 is y=5e^{-t/4}t