What is the solution for y^{''}+16y^'+100y=10,y(0)=0,y^'(0)=0 ?

The solution for y^{''}+16y^'+100y=10,y(0)=0,y^'(0)=0 is y=e^{-8t}(-1/10 cos(6t)-2/15 sin(6t))+1/10

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y^{''}+16y^'+100y=10,y(0)=0,y^'(0)=0

y^{^{''}} + 16 y^{^{'}} + 100 y = 10, y (0) = 0, y^{^{'}} (0) = 0

y = e^{- 8 t} (- \frac{1}{10} cos (6 t) - \frac{2}{15} sin (6 t)) + \frac{1}{10}

Solution steps

y^{''} (t) + 16 y^{'} (t) + 100 y = 10

Solve linear ODE:

y = e^{- 8 t} (- \frac{1}{10} cos (6 t) - \frac{2}{15} sin (6 t)) + \frac{1}{10}

y = e^{- 8 t} (- \frac{1}{10} cos (6 t) - \frac{2}{15} sin (6 t)) + \frac{1}{10}

y^{^{''}} + 4 y^{^{'}} + 3 y = cos (2 x)

y^{^{''}} + π^{2} y = \frac{5}{ln ( 10 )} sin (x ln (2))

\frac{d ^{2} y}{d t ^{2}} + 6 \frac{d y}{d t} + 9 y = e^{- 3 t}

y^{^{''}} + 2 y^{^{'}} + y = \frac{1}{x} e^{- x}

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

What is the solution for y^{''}+16y^'+100y=10,y(0)=0,y^'(0)=0 ?
The solution for y^{''}+16y^'+100y=10,y(0)=0,y^'(0)=0 is y=e^{-8t}(-1/10 cos(6t)-2/15 sin(6t))+1/10