2.1.45 \(y u_x+x u_y=0\) with \(u(0,y)=e^{-y^2}\). Problem 3.5(b) Lokenath Debnath

problem number 45

Added June 3, 2019.

Problem 3.5(b) nonlinear pde’s by Lokenath Debnath, 3rd edition.

Solve for \(u(x,y)\) \[ y u_x+x u_y=0 \] with \(u(0,y)=e^{-y^2}\)

Mathematica


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

Maple


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

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