2.1.64 \(y^2 u_x+(x y) u_y=x\) with \(u(x,1)=x^2\). Problem 3.14(f) Lokenath Debnath

problem number 64

Added June 3, 2019.

Problem 3.14(f) nonlinear pde’s by Lokenath Debnath, 3rd edition.

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

Mathematica


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

Maple


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

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