2.1.23 Recover a function from its gradient vector

problem number 23

Taken from Mathematica DSolve help pages

Solve for \(f(x,y)\) \begin {align*} \frac { \partial f}{\partial x} &= x y \cos (x y)+ \sin (x y) \\ \frac { \partial f}{\partial y} &= -e^{-y} +x^2 \cos (x y) \end {align*}

Mathematica


\[\left \{\left \{f(x,y)\to x \sin (x y)+e^{-y}+c_1\right \}\right \}\]

Maple


\[\{f \left (x , y\right ) = x \sin \left (x y \right )+c_{1}+{\mathrm e}^{-y}\}\]

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