solve the differential equation
dy/dx=x+y+1/2x+2y+3
Answers
Answered by
5
Answer:
ANSWER
dx
dy
=
2x+2y+3
x+y+1
Put x+y=v
1+
dx
dy
=
dx
dv
⇒
dx
dv
−1=
2v+3
v+1
⇒
dx
dv
=
2v+3
3v+4
⇒
3v+4
(2v+3)dv
=dx
Integrating both sides,
∫
3v+4
(2v+3)dv
=∫dx
⇒
3
1
∫
3v+4
2(3v+4)dv
+
3
1
∫
3v+4
1dv
=x+logc
⇒
3
2
v+
9
1
log3v+4=x+logc
⇒
9
1
log(3x+3y+4)−logc=
3
1
(x−2y)
⇒log
c
(x+y+
3
4
)
=3(x−2y)
x+y+
3
4
=ce
3(x−2y)
Comparing with given solution, we get
k=4
Similar questions