What is the solution for f^{''}(x)=6f^'(x)-6f(x) ?

The solution for f^{''}(x)=6f^'(x)-6f(x) is f(x)=c_{1}e^{(3+sqrt(3))x}+c_{2}e^{(3-sqrt(3))x}

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f^{''}(x)=6f^'(x)-6f(x)

f^{^{''}} (x) = 6 f^{^{'}} (x) - 6 f (x)

f (x) = c_{1} e^{(3 + 3) x} + c_{2} e^{(3 - 3) x}

Solution steps

f^{''} (x) = 6 f^{'} (x) - 6 f (x)

Solve linear ODE:

f (x) = c_{1} e^{(3 + 3) x} + c_{2} e^{(3 - 3) x}

f (x) = c_{1} e^{(3 + 3) x} + c_{2} e^{(3 - 3) x}

16 y^{^{''}} + 64 y = 0, y (0) = 0.3, y^{^{'}} (0) = - 0.2

y^{^{'''}} - y^{^{''}} - 9 y^{^{'}} + 9 y = 0

y^{^{''}} - 5 y + 6 y = 0

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} + 8 y = 0

y^{^{''}} + 2 y^{^{'}} = 0, y (0) = 14, y^{^{'}} (0) = - 10

What is the solution for f^{''}(x)=6f^'(x)-6f(x) ?
The solution for f^{''}(x)=6f^'(x)-6f(x) is f(x)=c_{1}e^{(3+sqrt(3))x}+c_{2}e^{(3-sqrt(3))x}