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7 Variational Principles
7.15 Prove: If at x = x 0 and x = x 1 , the appropriate boundary conditions are
satisfied, then the fourth-order differential equation
( py
)
+ (qy
)
+ r y = f (x)
can be transformed into a variational problem, where p, q, r and f (x) are the
known functions of x. What is the variational problem equivalent to the differential
equation? What are the necessary boundary conditions?
7 Variational Principles
7.15 Prove: If at x = x 0 and x = x 1 , the appropriate boundary conditions are
satisfied, then the fourth-order differential equation
( py
)
+ (qy
)
+ r y = f (x)
can be transformed into a variational problem, where p, q, r and f (x) are the
known functions of x. What is the variational problem equivalent to the differential
equation? What are the necessary boundary conditions?