What is the solution for 36y^{''}+156y^'+169y=0,y(0)=9,y^'(0)=4 ?

The solution for 36y^{''}+156y^'+169y=0,y(0)=9,y^'(0)=4 is y=9e^{-(13t)/6}+(47e^{-(13t)/6}t)/(2)

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36y^{''}+156y^'+169y=0,y(0)=9,y^'(0)=4

36 y^{^{''}} + 156 y^{^{'}} + 169 y = 0, y (0) = 9, y^{^{'}} (0) = 4

y = 9 e^{- \frac{13 t}{6}} + \frac{47 e ^{- \frac{13 t}{6}} t}{2}

Solution steps

36 y^{''} (t) + 156 y^{'} (t) + 169 y = 0

Solve linear ODE:

y = 9 e^{- \frac{13 t}{6}} + \frac{47 e ^{- \frac{13 t}{6}} t}{2}

y = 9 e^{- \frac{13 t}{6}} + \frac{47 e ^{- \frac{13 t}{6}} t}{2}

y^{^{''}} - 6 y = 0, y (0) = 0, y (1) = 0

y^{^{''}} - 2 y + y = 0, y (0) = x e^{x}

\frac{d ^{2} y}{d x ^{2}} + 10 \frac{d y}{d x} + 61 y = 0

77 y^{^{''''}} + 219 y^{^{''}} + 100 y = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = 5, y^{^{'}} (0) = 0

What is the solution for 36y^{''}+156y^'+169y=0,y(0)=9,y^'(0)=4 ?
The solution for 36y^{''}+156y^'+169y=0,y(0)=9,y^'(0)=4 is y=9e^{-(13t)/6}+(47e^{-(13t)/6}t)/(2)