2.1.52 \(x u_x+(x+y)u_y=u+1\) with \(u(x,0)=x^2\) Problem 3.5(i) Lokenath Debnath

problem number 52

Added June 3, 2019.

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

Solve for \(u(x,y)\) \[ x u_x+(x+y)u_y=u+1 \] With \(u(x,0)=x^2\).

Mathematica


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

Maple


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

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