What is the solution for y^{''}-14y^'+58y=0,y(0)=5,y^'(0)=-4 ?

The solution for y^{''}-14y^'+58y=0,y(0)=5,y^'(0)=-4 is y=e^{7t}(5cos(3t)-13sin(3t))

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y^{''}-14y^'+58y=0,y(0)=5,y^'(0)=-4

y^{^{''}} - 14 y^{^{'}} + 58 y = 0, y (0) = 5, y^{^{'}} (0) = - 4

y = e^{7 t} (5 cos (3 t) - 13 sin (3 t))

Solution steps

y^{''} (t) - 14 y^{'} (t) + 58 y = 0

Solve linear ODE:

y = e^{7 t} (5 cos (3 t) - 13 sin (3 t))

y = e^{7 t} (5 cos (3 t) - 13 sin (3 t))

x^{^{''}} + 8 x^{^{'}} + 25 x = 0

(D^{2} + 9) y = 0, Dy = 0, y = 2, x = 30

y^{^{''}} - 12 y^{^{'}} + 36 y = 0, y (0) = e^{6 x}

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

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

What is the solution for y^{''}-14y^'+58y=0,y(0)=5,y^'(0)=-4 ?
The solution for y^{''}-14y^'+58y=0,y(0)=5,y^'(0)=-4 is y=e^{7t}(5cos(3t)-13sin(3t))