User:Vijendra Rawat/Temp/Question Bank.doc

TEERTHANKER MAHAVEER UNIVERSITY

College of Engineering 

Question Bank-I

Solve the following differential equation 

Q.1.

Q. 2.

Q. 3.y”-y = 0.

Q. 4.

Q. 5.(1-x2)y”-xy’+4y = 0.

Q. 6.Solve in series

Q. 7.Solve in series

Q. 8.Solve in series

Q. 9.Solve in series

Q. 10.Solve in series

Q. 11.Solve in series

Q. 12.Solve in series

Q. 13.Solve in series

Q. 14.Transform the equation ,

By the substitution x =1/z and show that it has no integrals that are regular in

descending powers of x.

Q. 15.Prove that xP’9 = P’8 + 9P9.

Q. 16.Show that xP’n =nPn+(2n-3)Pn-2+(2n-7)Pn-4+………..

Q. 17.Show that 11(x2-1)P’5 = 30 (P6-P4).

Q. 18.Show that

Q. 19.Prove that

Q. 20.Prove that