Question

Solve(3x^+6xy)dx+(6x^y+4y3)Dy=0

Answer 1

Answer:

When solving the differential equation

(3x 2+6xy 2)dx+(6x 2y+4y 2)dy=0

I verified that it is an Exact Equation. By saying that

F x=3x 2+6xy 2 F y=6x 2y+4y 2

and integrating both sides I found

F(x,y)=3x 2y 2+4 3y 3+x 3=C

and since

y(0)=2

we have

3x 2y 2+4 3y 3+x 3=32 3

The problem is that the textbook's solution is

x 3+3x 2y 2+y 3=16

Thank you.