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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x \to 0 lim (\frac{x ^{3}}{x ^{6}})

\frac{\partial}{\partial y} (x^{2} + 2 y^{2} - x)

\int \frac{2 x - 3}{4 x - x ^{2}} d x

8

\int e^{t a n (4 x)} sec^{2} (4 x) d x

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