What is the solution for (dx)/(dt)=((e^t-e^{-t}))/(3+x),x(0)=0 ?

The solution for (dx)/(dt)=((e^t-e^{-t}))/(3+x),x(0)=0 is x=-3+sqrt(4cosh(t)+5)

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(dx)/(dt)=((e^t-e^{-t}))/(3+x),x(0)=0

\frac{d x}{d t} = \frac{( e ^{t} - e ^{- t} )}{3 + x}, x (0) = 0

x = - 3 + 4 cosh (t) + 5

Solution steps

\frac{d x}{d t} = \frac{( e ^{t} - e ^{- t} )}{3 + x}

Solve separable ODE:

x = - 3 + 4 cosh (t) + 5

x = - 3 + 4 cosh (t) + 5

What is the solution for (dx)/(dt)=((e^t-e^{-t}))/(3+x),x(0)=0 ?
The solution for (dx)/(dt)=((e^t-e^{-t}))/(3+x),x(0)=0 is x=-3+sqrt(4cosh(t)+5)