Page 139 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 5. Solve
2
d y dy 5x
3 2y e
dx 2 dx
2
d y x
6. 2 4y e sin2x
dx
Answers: Self Assessment

(y y 2 y y 1 ) (y y 2 y y 2 )
1
2
1
1
1. p 1 , p 2
(y y y y ) (y y 2 y y )
1 2
1 2
1 2
1
e 2x
2. Particular integral, P.I. =
3
3. y c e x c e 3x c e 5x
2
3
1
x
c
4. y e 4x ( cos3x c 2 sin 3 )
1
5. y (c 1 c 2 ) x e x c e 2x
3
6. y (c 1 c 2 ) x e x c 3 cos2x c 4 sin 2x
1 2x
3x
2x
7. y c e c e e
1
2
20
8. y c e x c e 2x c e 2x 1 e 3x
1
2
3
10
3x 1
9. y c e x /2 c e 2 e 2x
1
2
21
3 3 1 2x x
/2
x
x
10. y c e e c 2 cos x c 3 sin x e e 1
1
2 2 4
1
x
2x
x
11. y c e c e (cos2x 3sin2 )
2
1
20
1
3x
2x
12. y c e c e x (5 cos3x sin3 )
x
2
1
78
7.8 Further Readings
Books Yosida, K., Lectures in Differential and Integral Equations
Piaggio, H.T.H., Differential Equations
132 LOVELY PROFESSIONAL UNIVERSITY