27

Integrating (1), (2) and (3) w.r.t. x, y and z

respectively, we obtain

Solution

We have .....(1) 2 32 xyzyx

.....(2) 23 32zxxyy

.....(4) ),()2( 32232 zyfyzxxydxxyzy

.....(3) 34 223 yzxzz

.....(5) ),(3)23( 32232 zxgyzxxyydyzxxy

.....(6) ),()34( 324223 yxhyzxzdzyzxz

28

Comparing (4) with (5) and (6) we get

Czyzyf 43),(

Czyyzxxy 4322 3

To find constant C, use 2)0,0,0(

23 4322 zyyzxxy

Therefore

Problem 5

29

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