Page 357 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Differential and Integral Equation

2
Notes A Parabolic equation has ac = b , for example the diffusion equation
2  
K 2 0 ...(here y = t)
x y
2
A hyperbolic equation has ac < b , for example the wave equation
2 2
 1 
0 ...(here y is time)
x 2 c 2 y 2
21.6 Review Questions

1. Reduce the partial differential equation
2 2
 z  z
2 2 0
x  y 
to canonical form
2. Transform the partial differential equation into the form having constant coefficients

2  2 z  2 z 2  2 z
x 2xy y 0

x  2  x y  y 2
Answers: Self Assessment

2
 
1. 2 0 where ( , ) = z (x, y)

and = x y, = x + y.
2
  1  
2.
    
2
  
3. 2 0
 2 
where ( , ) = z(x, y)

21.7 Further Readings

Books Piaggio H.T.H, Differential Equations
Yosida K., Lectures in Differential and Integral Equations

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