Page 348 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Unit 20: Higher Order Equations with Constant Coefficients and Monge’s Method

Notes
3
4
x x
x
5. Z F 1 (y 2 ) F 2 (y 3 ) y
x
6 24
x 3 y 3
x
6. Z F 1 (y 2 ) F 2 (y x )
6 12
1 3
x
7. Z F 1 (y 2 ) F 2 (y x ) (x y )
36
1
8. Z F 1 (y ix ) F 2 (y ix ) 2 2 cos(mx xy )
(m n )
x 3 x 2
9. Z F 1 (y x ) x F 2 (x y ) (x y )
6 2
x 2
10. Z F 1 ( ) F 2 (y 2 ) x F 3 (y 2 ) sin(2x y )
x
y
x
4
11. Z F 1 (y x ) x F 2 (y x ) x sin y
12. Z F 1 (y 2 ) F 2 (y x ) y e x
x
13. Z F 1 (y ax ) e 2abx F 2 (y ax )
x
x
y
y
14. Z e F 1 ( ) e F 2 (y x ) 1 sin(x 2 )
2
15. Z F 1 (y 2 x 2 ) F 2 (y 2 x 2 )
y
16. Z F 1 (xy ) x F 2 xy log x
x
2
17. Z F 1 (x y ) F 2 (xy 2 )
z
x
18. y zx F 1 ( ) F 2 ( )
19. Z xy C x C y C 3
1
2
1 2 2
20. Z 2xy (x 3y ) C x (y mx )
1
2
20.13 Further Readings

Books Piaggio, H.T.H., Differential Equations
Sneddon L.N., Elements of Partial Differential Equations.

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