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

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

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(d^2x)/(dt^2)-x(dx)/(dx)=0

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

x = c_{1} e^{t} + c_{2} e^{- t}

Solution steps

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

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- t}

x = c_{1} e^{t} + c_{2} e^{- t}

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