2.1.66 \(u_x+u u_y=1\) with \(u(0,y)=a y\). Problem 3.16(a) Lokenath Debnath

problem number 66

Added June 3, 2019.

Problem 3.16(a) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \[ u_x+u u_y=1 \] With \(u(0,y)=a y\).

Mathematica


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

Maple


\[u \left (x , y\right ) = \frac {\left (x^{2}+2 y \right ) a +2 x}{2 a x +2}\]

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