#### 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

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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