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Category: Differential Equation

u-R-2-R-u-x-u-y-x-y-u-xy-

Question Number 324 by 123456 last updated on 25/Jan/15 $${u}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\frac{\partial{u}}{\partial{x}}+\frac{\partial{u}}{\partial{y}}=\frac{\left({x}+{y}\right){u}}{{xy}} \\ $$ Answered by prakash jain last updated on 21/Dec/14 $$\mathrm{The}\:\mathrm{equation}\:\mathrm{is}\:\mathrm{symmetric}\:\mathrm{in}\:{x},{y}. \\…

solve-x-dy-dx-y-x-

Question Number 224 by 123456 last updated on 25/Jan/15 $$\mathrm{solve} \\ $$$${x}\frac{{dy}}{{dx}}+{y}=\alpha{x}+\beta \\ $$ Answered by mreddy last updated on 16/Dec/14 $$\frac{{dy}}{{dx}}+\frac{{y}}{{x}}=\frac{\alpha{x}+\beta}{{x}} \\ $$$$\mathrm{Integrating}\:\mathrm{Factor}={e}^{\int\frac{\mathrm{1}}{{x}}{dx}} ={e}^{\mathrm{ln}\:{x}}…