What is the solution for y^{''}-6y^'+13y=0,y(0)=-3,y^'(0)=1 ?

The solution for y^{''}-6y^'+13y=0,y(0)=-3,y^'(0)=1 is y=e^{3t}(-3cos(2t)+5sin(2t))

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y^{''}-6y^'+13y=0,y(0)=-3,y^'(0)=1

y^{^{''}} - 6 y^{^{'}} + 13 y = 0, y (0) = - 3, y^{^{'}} (0) = 1

y = e^{3 t} (- 3 cos (2 t) + 5 sin (2 t))

Solution steps

y^{''} (t) - 6 y^{'} (t) + 13 y = 0

Solve linear ODE:

y = e^{3 t} (- 3 cos (2 t) + 5 sin (2 t))

y = e^{3 t} (- 3 cos (2 t) + 5 sin (2 t))

What is the solution for y^{''}-6y^'+13y=0,y(0)=-3,y^'(0)=1 ?
The solution for y^{''}-6y^'+13y=0,y(0)=-3,y^'(0)=1 is y=e^{3t}(-3cos(2t)+5sin(2t))