2.1.59 \(u_x+x u_y=y\) with \(u(1,y)=2 y\) Problem 3.9(b) Lokenath Debnath

problem number 59

Added June 3, 2019.

Problem 3.9(b) nonlinear pde’s by Lokenath Debnath, 3rd edition.

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

Mathematica


\[\left \{\left \{u(x,y)\to -\frac {x^3}{3}-\frac {x^2}{2}+x y+y+\frac {5}{6}\right \}\right \}\]

Maple


\[u \left (x , y\right ) = -\frac {1}{3} x^{3}-\frac {1}{2} x^{2}+x y +y +\frac {5}{6}\]

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