2.1.31 \(u_x-u_y=1\) with \(u(x,0)=x^2\) Example 3.5.6 in Lokenath Debnath

problem number 31

Added June 2, 2019.

From example 3.5.6, page 214 nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \begin {align*} u_x-u_y&=1 \end {align*}

with \(u(x,0)=x^2\)

Mathematica


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

Maple


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

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