Page 347 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 20.12 Review Questions

1. Solve
4 4
z z 0
x 4 y 4

2. Solve
2
(D 3 3D D 2DD 2 ) z 0
3. Solve
2 2 2
z z 2 z
2a a 0
x 2 x y y 2
4. Solve
4 4 4 4 4
z 2 z 3 z 8 z 4 z 0
2
3
x 4 x y x y 2 x y 3 y 4
5. Solve
2 2 2
z z z
(a b ) ab xy
x 2 x y y 2
6. Solve
2 2 2
z 2 z z e x 2y
x 2 x y y 2
7. Solve

2 2
z z z z cos(x 2 ) e y
y
x 2 x y y
8. Solve
(DD D D 1)z xy
9. Solve

2 z 2 z
2
x 2 2 y 2 2 x y
x y
10. Solve
r t (rt s 2 ) 1

Answers: Self Assessment

x
x
1. Z F 1 (y mx ) F 2 (y 3 ) F 3 (y 2 )
x
x
2. Z F y F 2 (y 2 )
1
2
x
3. Z F 1 ( ) F 2 (y 2 ) xF 3 (y 2 )
x
y
x
x
4. Z F 1 (y 3 ) x F 2 (y 3 )
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