Please see the step enclosed in yellow ring in the above image. My question is why we cannot apply Componendo-Dividendo so the integration becomes easy.
The correct answer to the question is (x - y)^2 = Cxy × e^(-y/x) but I do not get this answer by applying Componend-Dividendo.
Why am I not getting correct answer? Please help.
Here is what I did :
Edited: The issue is in the very first step. Componendo and dividendo are applicable to equations where both sides of the equation are rational expressions. In other words, if we know that $$\frac{a}{b}=\frac{c}{d}$$ where neither side is equal to $1$ then componendo and dividendo let us conclude that $$\frac{a+b}{a-b}=\frac{c+d}{c-d}.$$
They are not applicable to individual rational expressions. Indeed, if we could do as you are saying, then $$\frac32=\frac{3+2}{3-2}=\frac{5}{1},$$ which is clearly absurd.