Page 429 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 24.6 Keywords

Integral equation is an equation in which the unknown variable appears under the integral sign.
The conversion of a differential equation into an integral equation is possible if the function and
its first derivatives are continuous in the interval.

24.7 Review Questions

1. Express the differential equation

y 2y 8y 0
with boundary conditions (0) 0y y (1) as in integral equation.

2. Convert the differential equation

x
y 2y 8y 5x 2 3 ,
with (0)y 2, y (0) 3 into integral equation.

Answers: Self Assessment

x d y
2
G
x
t
1. G ( ) (x 3 x 4x 2 ) ( )dt 1 3x 4x 2 2, with ( )G x
dx 2
0
t
2. 2 ( ) ( 2t 2u 3) ( )du 4 e x 2 cosx 10t 6
y
y
x
u
0
24.8 Further Readings
Books Louis A. Pipes and Lawrence R. Harnvill, Applied Mathematics for Engineers
and Physicists
Tricomi, P.G., Integral Equation
Yosida, K., Lectures in Differential and Integral Equations

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