What is the solution for y^{''}-8y^'+17y=0,y(0)=-4,y^'(0)=-1 ?

The solution for y^{''}-8y^'+17y=0,y(0)=-4,y^'(0)=-1 is y=e^{4t}(-4cos(t)+15sin(t))

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y^{''}-8y^'+17y=0,y(0)=-4,y^'(0)=-1

y^{^{''}} - 8 y^{^{'}} + 17 y = 0, y (0) = - 4, y^{^{'}} (0) = - 1

y = e^{4 t} (- 4 cos (t) + 15 sin (t))

Solution steps

y^{''} (t) - 8 y^{'} (t) + 17 y = 0

Solve linear ODE:

y = e^{4 t} (- 4 cos (t) + 15 sin (t))

y = e^{4 t} (- 4 cos (t) + 15 sin (t))

y^{^{''}} + 7 y^{^{'}} - 2 y = 0

8 y^{^{''}} + 4 y^{^{'}} + y = 0

y^{^{''}} - 12 y^{^{'}} + 32 y = 0

2 y^{^{'''}} - 3 y^{^{''}} + y^{^{'}} = 0

y^{^{'''}} + 7 y^{^{''}} + 16 y^{^{'}} + 12 y = 0

What is the solution for y^{''}-8y^'+17y=0,y(0)=-4,y^'(0)=-1 ?
The solution for y^{''}-8y^'+17y=0,y(0)=-4,y^'(0)=-1 is y=e^{4t}(-4cos(t)+15sin(t))