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

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

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(e^t+e^{-t})(dx)/(dt)=x^2

(e^{t} + e^{- t}) \frac{d x}{d t} = x^{2}

x = - \frac{1}{arctan ( e ^{t} ) + c _{1}}

Solution steps

(e^{t} + e^{- t}) \frac{d x}{d t} = x^{2}

Solve separable ODE:

x = - \frac{1}{arctan ( e ^{t} ) + c _{1}}

x = - \frac{1}{arctan ( e ^{t} ) + c _{1}}

x^{2} y^{^{''}} + x y^{^{'}} + y = 0

\int 5 sec^{3} (x) d x

\frac{d}{d x} (e^{2 x} sin (2 x))

\frac{d}{d x} (\frac{( x )}{x + 1})

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

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