What is the solution for y^{''}+4y^'+13y=0,y(pi/2)=0,y^'(pi/2)=9 ?

The solution for y^{''}+4y^'+13y=0,y(pi/2)=0,y^'(pi/2)=9 is y=3e^{pi-2t}cos(3t)

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y^{''}+4y^'+13y=0,y(pi/2)=0,y^'(pi/2)=9

y^{^{''}} + 4 y^{^{'}} + 13 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

y = 3 e^{π - 2 t} cos (3 t)

Solution steps

y^{''} (t) + 4 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = 3 e^{π - 2 t} cos (3 t)

y = 3 e^{π - 2 t} cos (3 t)

y^{^{''}} - 6 y^{^{'}} + 14 y = 0

y^{^{''}} - y^{^{'}} + 6 y = 0

x^{^{''}} + a^{2} x = 0

y^{^{''}} - 14 y^{^{'}} + 40 y = 0

y^{^{''}} - 2 y^{^{'}} + 10 y = 0, y (0) = 4, y^{^{'}} (0) = 5

What is the solution for y^{''}+4y^'+13y=0,y(pi/2)=0,y^'(pi/2)=9 ?
The solution for y^{''}+4y^'+13y=0,y(pi/2)=0,y^'(pi/2)=9 is y=3e^{pi-2t}cos(3t)