What is the solution for y^{''}+4y^'+20y=0,y(pi)=7,y(0)=8 ?

The solution for y^{''}+4y^'+20y=0,y(pi)=7,y(0)=8 is y=e^{-2t}(7e^{2pi}cos(4t)+c_{2}sin(4t))

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y^{''}+4y^'+20y=0,y(pi)=7,y(0)=8

y^{^{''}} + 4 y^{^{'}} + 20 y = 0, y (π) = 7, y (0) = 8

y = e^{- 2 t} (7 e^{2 π} cos (4 t) + c_{2} sin (4 t))

Solution steps

y^{''} (t) + 4 y^{'} (t) + 20 y = 0

Solve linear ODE:

y = e^{- 2 t} (7 e^{2 π} cos (4 t) + c_{2} sin (4 t))

y = e^{- 2 t} (7 e^{2 π} cos (4 t) + c_{2} sin (4 t))

y \cdot u^{2} - y^{^{''}} = 0

2 y^{^{''}} + 3 y^{^{'}} - 2 y = 0, y (0) = 1, y^{^{'}} (0) = 7

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y^{^{'}} (0) = 0

y^{^{''}} + 3 y^{^{'}} + 2 y = 0, y^{^{'}} (0) = 1

5 y^{^{''}} + 9 y^{^{'}} - 14 y = 0

What is the solution for y^{''}+4y^'+20y=0,y(pi)=7,y(0)=8 ?
The solution for y^{''}+4y^'+20y=0,y(pi)=7,y(0)=8 is y=e^{-2t}(7e^{2pi}cos(4t)+c_{2}sin(4t))