
8-48 Diff erential Equations
11. yp + xq + pq = 0. [Marathwada 1993]
Ans:
22
2
1
a
zax y c
a
=− +
+
12. p + q = sin x + sin y.
[Madras 1993, Karnataka 1993]
Ans: z = a
(x − y) − (cos x + cos y) + c
13. z = px + qy + p
2
+ q
2
.
Ans: z = ax + by + a
2
+ b
2
14.
22
1zpxqy p q=++ ++l
.
Ans:
22
1zaxby a b=++ ++l
15. z = px + qy + sin(p + q).
Ans: z = ax +
by + sin(a + b)
8.12 EULER’S METHOD OF SEPARATION
OF VARIABLES
When we model scientific, engineering, biotechno logical and other
processes there arise initial and boundary value problems involving
partial different ial equations. The general solutions of these partial
differential equations are in the form of arbitrary ...