Page 257 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes
v 3 2 dx
or 2 dv
( v v 1)(v v 1) x
2 1 2v 1
or 2 dv log cx
v v 1 v v 1

(v 1)(v 2 v 1)
or log 2 logcx
v

(y x y 2 xy x 2
)
or cx
3 y 2
x 2
x
2 2
x y
or 3 3 . k
x y
dx /x dy /y dz
Also 3 3 3 3 .
y 2x 2y x 9z x 3 y 3

dx /x dy /y dz
.
1 3z
3 log x + 3 log y = log cz
3 3
or x y = 1/cz.
1 x y
z 3 3 2 2 .
x y y x

(y z )p (z x )q x y
Example 7: Solve: .
yz zx xy
Solution:

(xy zx) p + (yz yx) q = zx zy.

dx dy dz
.
y zx yz yx zx zy
dx + dy + dz = 0
or x + y + z = c .
1
Also yz dx + zx dy + xy dz = 0.

dx dy dz
or 0.
x y z
log x + log y + log z = log c .
2
xyz = c .
2

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