Page 250 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Unit 16: Classifications of Integrals of the First Order Partial Differential Equations

16.7 Review Questions Notes

1. Eliminate the arbitrary constants a, b from the equation
2
zx = ax + by a b
2. Show that
2
2
2
2
z = ax + by 3a + b 2
is the complete integral of the equation
3
2 2 2
3 2
2
(z px qy)x y = q zx 3p z y
Find the singular integral.
Answers: Self Assessment
1. ( z px qy ) z 2 1 0

2. ( z q p ) y x 0

5. (y 2 z 2 x 2 )p 2xyq 2xz 0

6. zx y

16.8 Further Readings

Books Piaggio, H.T.H., Differential Equations
Sneddon, L.N., Elements of Partial Differential Equations
Yosida, K., Lectures in Differential and Integral Equations

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