Page 208 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

Unit 12: Sturm Comparison and Separation Theorems

3. If u , u are linearly independent solution of y + p(x)y + q(x)y = 0 and y is any other Notes
1 2
solution, show that Wronskian of (y, u , u )
1 2
y u 1 u 2
W(x) = y u 1 u 2
y u 1 u 2

is zero.

Answers: Self Assessment

cosx
1.
x
complete solution is (A sin x + B cos x)/x
2. y = A sin 2x + B cos 2x + x cos 2x sin 2x log (cos 2x)
3. 3x 2

12.10 Further Readings

Books Pipes, Louis A. & Lawrence R. Harvill, Applied Mathematics for Engineers &
Physicists
King A.C., Billingham, J. Otto S.R., Differential Equations.

Yosida, K., Lectures on Differential and Integral Equations
Sneddon, L.N., Elements of partial differential equations

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