Question

solve for solution
y.dx+(x+x^2).dy=0​

Answer 1

Step-by-step explanation:

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

x^2dx + y dx + y^2 dy+ x dy = 0

x^2dx + y^2 dy+ y dx+ x dy = 0

x^2dx + y^2 dy+ d(x*y) = 0

d(1/3 x^3) + d(1/3 y^3)+ d(x*y) = 0

(1/3)* x^3 + (1/3)* y^3+ x*y = C1

x^3 + y^3+3* x*y = C where C=3C1