Find Integrating factor of dy = {[e^(x-y)] ( e^x-e^y)} dx is
Answers
Answered by
0
Answer:
Correct option is
C
e
y
=c.exp(−e
x
)+e
x
−1
dx
dy
=e
x−y
(e
x
−e
y
)
dx
dy
=
e
y
e
x
(e
x
−e
y
)
e
y
dx
dy
=e
2x
−e
x
e
y
e
y
dx
dy
+e
x
e
y
=e
2x
Put e
y
=v
e
y
dx
dy
=
dx
dv
e
y
dx
dv
+ve
x
=e
2x
which is a linear differential eqn with v as dependent variable.
Here, P=e
x
;Q=e
2x
Integrating factor $$I.F.=e^\int{e^x}dx =e^{e^x}$$
So, the solution of given differential eqn is
v.e
e
x
=∫e
e
x
e
2x
dx+C
Put e
x
=t in the above integral
⇒e
x
dx=dt
v.e
e
x
=∫e
t
tdt+C
⇒e
y
e
e
x
=te
t
−e
t
+C
⇒e
y
e
e
x
=e
x
e
e
x
−e
e
x
+C
⇒e
y
=e
x
−1+Ce
−e
x
Similar questions