Question

Solve (x+y)^2 dx+(x+y)^2 dy=0.

Answer 1

integral of (x+y)^2 dx=(x+y)^3/3+g(y)=C
(x+y)^2+g'(y)=(x+y)^2
g'(y)=0
g(y)=0
(x+y)^3/3=C
But the answer in the book is x+y=C. So which answer is right?

Answer 2

@amistre64

Answer 3

g(y) = C since g'(y) = 0

so the solution is: (x+y)^3/3 + C is the family of solutions

Answer 4

Thank you!

Answer 5

youre welcome