What is the solution for y^{''}-14y^'+85y=0,y(0)=2,y^'(0)=-4 ?

The solution for y^{''}-14y^'+85y=0,y(0)=2,y^'(0)=-4 is y=e^{7t}(2cos(6t)-3sin(6t))

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y^{''}-14y^'+85y=0,y(0)=2,y^'(0)=-4

y^{^{''}} - 14 y^{^{'}} + 85 y = 0, y (0) = 2, y^{^{'}} (0) = - 4

y = e^{7 t} (2 cos (6 t) - 3 sin (6 t))

Solution steps

y^{''} (t) - 14 y^{'} (t) + 85 y = 0

Solve linear ODE:

y = e^{7 t} (2 cos (6 t) - 3 sin (6 t))

y = e^{7 t} (2 cos (6 t) - 3 sin (6 t))

x^{^{''}} - 2 a x^{^{'}} + a^{2} x = 0

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

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

y^{^{''}} + 0.6 y^{^{'}} + 8 y = 0

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

What is the solution for y^{''}-14y^'+85y=0,y(0)=2,y^'(0)=-4 ?
The solution for y^{''}-14y^'+85y=0,y(0)=2,y^'(0)=-4 is y=e^{7t}(2cos(6t)-3sin(6t))