What is the solution for y^{''}+6y^'+10y=0,y(pi/2)=0,y^'(pi/2)=9 ?

The solution for y^{''}+6y^'+10y=0,y(pi/2)=0,y^'(pi/2)=9 is y=-9e^{(3pi)/2-3t}cos(t)

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y^{''}+6y^'+10y=0,y(pi/2)=0,y^'(pi/2)=9

y^{^{''}} + 6 y^{^{'}} + 10 y = 0, y (\frac{π}{2}) = 0, y^{^{'}} (\frac{π}{2}) = 9

y = - 9 e^{\frac{3 π}{2} - 3 t} cos (t)

Solution steps

y^{''} (t) + 6 y^{'} (t) + 10 y = 0

Solve linear ODE:

y = - 9 e^{\frac{3 π}{2} - 3 t} cos (t)

y = - 9 e^{\frac{3 π}{2} - 3 t} cos (t)

What is the solution for y^{''}+6y^'+10y=0,y(pi/2)=0,y^'(pi/2)=9 ?
The solution for y^{''}+6y^'+10y=0,y(pi/2)=0,y^'(pi/2)=9 is y=-9e^{(3pi)/2-3t}cos(t)