Answer:
let M=ex +y and N=2 +x +yey
(a) σM/σy =1 and σN/σx = 1
since σM/σy = σN/σx , it is an exact equation
(b) ∫M dx + ∫terms of N not containing x
∫(ex + y) dx +∫yey + 2 dy
xy + ex +yey -ey +2y=C
(c) using y(0)=1
C=3
(d) from the differential equation given
by dividing through by dx
dy/dx = (-y-ex) /(2+x+yey)
from the solution
(xy + ex +yey -ey =2y)=
(3)
x + y + ex + yey
+ ey
- ey
+ 2
= 0
= (-y-ex) /(2+x+yey)
Step-by-step explanation:
1. integrate with respect to x keeping y constant
2. integrate terms without x in N
3. Result of 1 + result 2= C
4. insert the condition given into 3
5. compare the solution of 4 to the differential equation