(1) SINGULAR INTEGRALS –SOLUTION OF
STANDARD
TYPES OF FIRST ORDER PARTIAL DIFFERENTIAL
EQUATIONS
III.
(a) Problems based on General solution of p.d.e in ordinary cases:
Example
1.3 (a) (1): Solve dz/dx
= sin x.
Example
1.3 (a) (2): Find the general solution of d2z/dy2
= 0.
Example
1.3(a)(3): Solve d2z/dx
dy = 0.
Example
1.3(a) (4): Solve d2z/dx dy = sinx.
Example
1.3(a) (5): Solve : d2z/dx
dy = sin y.
Example
1.3(a) (6): Example
1.3(a) (6): Solve d2z/dx2 = a2 given that x=0, dz/dx = a sin
y and dz/dy =0.
Since z is a function of x and y.
Therefore A & B will be the functions of y alone. Hence