What is the solution for (df)/(dx)+f(x)^2=0 ?

The solution for (df)/(dx)+f(x)^2=0 is f(x)=e^{-(x^3)/3+c_{1}}

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(df)/(dx)+f(x)^2=0

\frac{df}{d x} + f (x)^{2} = 0

f (x) = e^{- \frac{x ^{3}}{3} + c_{1}}

Solution steps

\frac{df}{d x} + f x^{2} = 0

Solve separable ODE:

f (x) = e^{- \frac{x ^{3}}{3} + c_{1}}

f (x) = e^{- \frac{x ^{3}}{3} + c_{1}}

\frac{d y}{d x} = \frac{y ln ( y )}{cot ( x )}

y (4 + x^{2}) d y - x (2 + y^{2}) d x = 0

\frac{d y}{d x} x ln (x) - y = 0, y (2) = ln (4)

y^{^{'}} = y (1 + \frac{1}{x})

\frac{d v}{d u} = tan (v)

What is the solution for (df)/(dx)+f(x)^2=0 ?
The solution for (df)/(dx)+f(x)^2=0 is f(x)=e^{-(x^3)/3+c_{1}}