What is the solution for y^{''}-14y^'+65y=0,y(0)=4,y^'(0)=-4 ?

The solution for y^{''}-14y^'+65y=0,y(0)=4,y^'(0)=-4 is y=e^{7t}(4cos(4t)-8sin(4t))

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y^{''}-14y^'+65y=0,y(0)=4,y^'(0)=-4

y^{^{''}} - 14 y^{^{'}} + 65 y = 0, y (0) = 4, y^{^{'}} (0) = - 4

y = e^{7 t} (4 cos (4 t) - 8 sin (4 t))

Solution steps

y^{''} (t) - 14 y^{'} (t) + 65 y = 0

Solve linear ODE:

y = e^{7 t} (4 cos (4 t) - 8 sin (4 t))

y = e^{7 t} (4 cos (4 t) - 8 sin (4 t))

- a y^{^{''}} + b y^{^{'}} + cy = 0

y^{^{''}} - 3 y^{^{'}} - 18 y = 0, y (0) = 24

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

1 y^{^{''}} + 0 y^{^{'}} + 9 y = 0, y (0) = 6, y^{^{'}} (0) = - 17

\frac{\frac{d ^{2} f}{d x ^{2}}}{f ( x )} = 1

What is the solution for y^{''}-14y^'+65y=0,y(0)=4,y^'(0)=-4 ?
The solution for y^{''}-14y^'+65y=0,y(0)=4,y^'(0)=-4 is y=e^{7t}(4cos(4t)-8sin(4t))