What is the solution for f^{'''}+f^{''}+3f^'-5f=0 ?

The solution for f^{'''}+f^{''}+3f^'-5f=0 is f(t)=c_{1}e^t+e^{-t}(c_{2}cos(2t)+c_{3}sin(2t))

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f^{'''}+f^{''}+3f^'-5f=0

f^{^{'''}} + f^{^{''}} + 3 f^{^{'}} - 5 f = 0

f (t) = c_{1} e^{t} + e^{- t} (c_{2} cos (2 t) + c_{3} sin (2 t))

Solution steps

f^{'''} (t) + f^{''} (t) + 3 f^{'} (t) - 5 f (t) = 0

Solve linear ODE:

f (t) = c_{1} e^{t} + e^{- t} (c_{2} cos (2 t) + c_{3} sin (2 t))

f (t) = c_{1} e^{t} + e^{- t} (c_{2} cos (2 t) + c_{3} sin (2 t))

s - 1

\int \frac{3 x}{( x ^{2} + 3 ) ^{\frac{1}{3}}} d x

\frac{d}{d x} (\frac{( 1 - x ^{2} )}{2 - x})

x \to 3 - lim (\frac{1}{∣ x - 3 ∣})

\int_{0}^{9} x d x

What is the solution for f^{'''}+f^{''}+3f^'-5f=0 ?
The solution for f^{'''}+f^{''}+3f^'-5f=0 is f(t)=c_{1}e^t+e^{-t}(c_{2}cos(2t)+c_{3}sin(2t))