Question

The general solution of the differential equation $(x^2+y^2+2x)dx+2ydy=0,$ is ______ (K is constant of integration)

• A. $y+{\log }_e(x^2+y^2)=k$
• B. $x+{\log }_e(x^2+y^2)=k$
• C. $y^2+x{\log }_e(x^2+y^2)=k$
• D. $x^2+y{\log }_e(x^2+y^2)=k$

Answer 1

The correct option is B $x+{\log }_e(x^2+y^2)=k$

$(x^2+y^2)dx+(2xdx+2ydy)=0(x^2+y^2)dx+d(x^2+y^2)=0\int dx+\int \frac{d(x^2+y^2)}{x^2+y^2}=0\Rightarrow x+lo{g}_e(x^2+y^2)=k$