2.1.58 \(u_x+x u_y=y\) with \(u(0,y)=y^2\) Problem 3.9(a) Lokenath Debnath

problem number 58

Added June 3, 2019.

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

Solve for \(u(x,y)\) \[ u_x+x u_y=y \] With \(u(0,y)=y^2\).

Mathematica


\[\left \{\left \{u(x,y)\to -x^2 y+\frac {x^4}{4}-\frac {x^3}{3}+x y+y^2\right \}\right \}\]

Maple


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

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