What is the solution for y^{''}-10y^'+34y=0,y(0)=5,y^'(0)=-2 ?

The solution for y^{''}-10y^'+34y=0,y(0)=5,y^'(0)=-2 is y=e^{5t}(5cos(3t)-9sin(3t))

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y^{''}-10y^'+34y=0,y(0)=5,y^'(0)=-2

y^{^{''}} - 10 y^{^{'}} + 34 y = 0, y (0) = 5, y^{^{'}} (0) = - 2

y = e^{5 t} (5 cos (3 t) - 9 sin (3 t))

Solution steps

y^{''} (t) - 10 y^{'} (t) + 34 y = 0

Solve linear ODE:

y = e^{5 t} (5 cos (3 t) - 9 sin (3 t))

y = e^{5 t} (5 cos (3 t) - 9 sin (3 t))

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

4 y^{^{''}} + 28 y = 0, y (0) = 3, y^{^{'}} (0) = 7

y^{^{'''}} + y = 0, y (0) = 0, y^{^{'}} (0) = 1, y^{^{''}} (0) = 2

(D^{2} + 2 D^{2} + D + 2) y = 0

y^{^{'''}} + 7 y^{^{''}} + 10 y^{^{''}} = 0

What is the solution for y^{''}-10y^'+34y=0,y(0)=5,y^'(0)=-2 ?
The solution for y^{''}-10y^'+34y=0,y(0)=5,y^'(0)=-2 is y=e^{5t}(5cos(3t)-9sin(3t))