2.1.50 \(x u_x+y u_y=u+1\) with \(u=x^2\) on \(y=x^2\) Problem 3.5(g) Lokenath Debnath

problem number 50

Added June 3, 2019.

Problem 3.5(g) nonlinear pde’s by Lokenath Debnath, 3rd edition.

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

Mathematica


\[\left \{\left \{u(x,y)\to \frac {x^2}{y}+y-1\right \}\right \}\]

Maple


\[u \left (x , y\right ) = x \mathit {\_F1} \left (\frac {y}{x}\right )-1\]

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