2.1.38 \((1+x^2) u_x+ u_y=0\) Problem 3.3(d) Lokenath Debnath

problem number 38

Added June 2, 2019.

Problem 3.3(d) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \[ (1+x^2) u_x+ u_y=0 \]

Mathematica


\[\left \{\left \{u(x,y)\to c_1\left (y-\tan ^{-1}(x)\right )\right \}\right \}\]

Maple


\[u \left (x , y\right ) = \mathit {\_F1} \left (y -\arctan (x )\right )\]

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