u-R-2-R-u-x-x-2-y-2-2xu-0-

Question Number 293 by 123456 last updated on 25/Jan/15

u : R^{2} \to R

\frac{\partial u}{\partial x} (x^{2} + y^{2}) + 2 x u = 0

Answered by prakash jain last updated on 19/Dec/14

\frac{d u}{u} = \frac{2 x d x}{x^{2} + y^{2}}

x^{2} + y^{2} = t \Rightarrow 2 x d x = d t

\ln u = \ln t + C = \ln (x^{2} + y^{2}) + C

u = (x^{2} + y^{2}) \cdot C_{1}