2.1.47 \(u_x+x u_y=0\) with \(u(0,y)=\sin y\). Problem 3.5(d) Lokenath Debnath

problem number 47

Added June 3, 2019.

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

Solve for \(u(x,y)\) \[ u_x+x u_y=0 \] with \(u(0,y)=\sin y\).

Mathematica


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

Maple


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

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