Question

The general solution of the differential equation \( (x-y)dy=(x+y)dx \) is

• A. \( \tan^{-1}\left(\frac{y}{x}\right)=c\sqrt{x^2+y^2} \)
• B. \( \tan^{-1}\left(\frac{y}{x}\right)=x^2+y^2+c \)
• C. \( e^{\tan^{-1}\left(\frac{y}{x}\right)}=\dfrac{c\sqrt{x^2+y^2}}{x} \)
• D. \( e^{\tan^{-1}\left(\frac{y}{x}\right)}=c\sqrt{x^2+y^2} \)

Hint:

For homogeneous differential equations, use the substitution \(y=vx\), then separate variables and integrate.

Answer 1

The Correct Option is D