Page 451 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

Notes 27.4 Keywords

The relation between the Volterra integral equation and linear differential equation with initial
condition has to be understood.

Method of conversion of differential equation to integral equation shows that the solution is
unique as we show that the new integral equation satisfies the original differential equation.

27.5 Review Questions

1. Convert the differential equation

2
x
x
y ( ) xy ( ) x y ( ) 1 x
x
with y(0) = 4, y (0) = 2, into integral equation.
2. Convert the differential equation
x 3
x
y
x
y
x
y ( ) 3 ( ) 2 ( ) 4 x
6
with y(0) = 1, y (0) = 2
Answers: Self Assessment
3
x d y
2
u
x
G
x
1. G ( ) 3 (x ) u G ( )du 18x 24 3x 2 with ( ) 3
0 dx
2. y iv ( ) 6y ( ) 6 ( ) 12 ( ) 3cos x
x
y
x
x
x
y
27.6 Further Readings
Books Tricomi, F.G., Integral Equations
Yosida, K., Lectures in Differential and Integral Equations

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