Solve the following differential eq...
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Solve the following differential equations: 1. (xy2 + x)dx + (yx² + y)dy = 0.

JEE/Engineering Exams
Maths
Solution
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( left(x y^{2}+xright) d x+left(y x^{2}+yright) d y=0 ) ( x d xleft(y^{2}+1right)=-y d yleft(x^{2}+1right) ) ( frac{x}{x^{2}+1} d x=frac{-y}{y^{2}+1} d y ) Integrating both sides ( int frac{x}{x^{2}+1} d x=-int frac{y^{2}}{y^{2}+1} d y ) ( Rightarrow frac{log left|x^{2}+1right|}{2}=-frac{log left|y^{2}+1right|}{2}+C^{prime} ) ( Rightarrow operatorname{cog}left|x^{2}+1right|+log left|y^{2}+1right|=c )
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