What is the solution for 4(d^2x)/(dt^2)-1(dx)/(dt)-3x=0,x(0)=1 ?

The solution for 4(d^2x)/(dt^2)-1(dx)/(dt)-3x=0,x(0)=1 is x=(1-c_{2})e^t+c_{2}e^{-(3t)/4}

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4(d^2x)/(dt^2)-1(dx)/(dt)-3x=0,x(0)=1

4 \frac{d ^{2} x}{d t ^{2}} - 1 \frac{d x}{d t} - 3 x = 0, x (0) = 1

x = (1 - c_{2}) e^{t} + c_{2} e^{- \frac{3 t}{4}}

Solution steps

4 \frac{d ^{2} x}{d t ^{2}} - 1 \frac{d x}{d t} - 3 x = 0

Solve linear ODE:

x = (1 - c_{2}) e^{t} + c_{2} e^{- \frac{3 t}{4}}

x = (1 - c_{2}) e^{t} + c_{2} e^{- \frac{3 t}{4}}

arctan (- 6 x)

4 t^{2} cos (2 t) + 5 t e^{- 7 t}

f (x) = \frac{c ^{5} - x ^{5}}{c ^{5} + c ^{5}}

f^{^{'}} (t) - f (t) = 6 t

What is the solution for 4(d^2x)/(dt^2)-1(dx)/(dt)-3x=0,x(0)=1 ?
The solution for 4(d^2x)/(dt^2)-1(dx)/(dt)-3x=0,x(0)=1 is x=(1-c_{2})e^t+c_{2}e^{-(3t)/4}