What is the solution for y^{''}-4y^'+13y=0,y(0)=-2,y^'(0)=-16 ?

The solution for y^{''}-4y^'+13y=0,y(0)=-2,y^'(0)=-16 is y=e^{2t}(-2cos(3t)-4sin(3t))

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y^{''}-4y^'+13y=0,y(0)=-2,y^'(0)=-16

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 2, y^{^{'}} (0) = - 16

y = e^{2 t} (- 2 cos (3 t) - 4 sin (3 t))

Solution steps

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

Solve linear ODE:

y = e^{2 t} (- 2 cos (3 t) - 4 sin (3 t))

y = e^{2 t} (- 2 cos (3 t) - 4 sin (3 t))

What is the solution for y^{''}-4y^'+13y=0,y(0)=-2,y^'(0)=-16 ?
The solution for y^{''}-4y^'+13y=0,y(0)=-2,y^'(0)=-16 is y=e^{2t}(-2cos(3t)-4sin(3t))