homogenic equation: xyy' = (x + y)^2, y(1) = 0

[ibanez1608]

. . . . .\(\displaystyle \begin{cases}xyy'\, =\, (x\, +\, y)^2 \\ y(1)\, =\, 0\end{cases}\). . .\(\displaystyle 2.1\)

please help i dont know how to start to separate

 

[Caesium]

Hint: Rearrange & look at it!

. . . . .\(\displaystyle \begin{cases}xyy'\, =\, (x\, +\, y)^2 \\ y(1)\, =\, 0\end{cases}\). . .\(\displaystyle 2.1\)

please help i dont know how to start to separate

In such problems, it helps to separate the differential terms (y') and algebraic terms (x, y & their functions). So, rewrite the given equation in y' = f(x,y). Now, what do you notice about the degree of the polynomials in the numerator & denominator? Does that help you think of the next step/suitable substitution?