Question

The general solution of the differential equation \[ y(2x+y)\,dx=x(x+y)\,dy \] is

• A. \[ \log\left(\frac{cx^2}{y}\right)+\frac{y}{x}=0 \]
• B. \[ \log\left(\frac{y}{cx^2}\right)+\frac{y}{x}=0 \]
• C. \[ \log(cx^2y^2)+\frac{y}{x}=0 \]
• D. \[ \log(cx^2y)+\frac{y}{x}=0 \]

Hint:

Whenever a differential equation is homogeneous, use \[ y=vx \] (or \(x=vy\)). This converts the equation into a separable differential equation in \(v\) and \(x\).

Answer 1

The Correct Option is B