User:Vijendra Rawat/B.Tech Second Year

TEERTHANKER MAHAVEER UNIVERSITY College of Engineering

Question Bank-I

Solve the following differential equation

Q.1. [[Image:]]

Q. 2.[[Image:]]

Q. 3.y”-y = 0.

Q. 4.[[Image:]]

Q. 5.(1-x²)y”-xy’+4y = 0.

Q. 6.Solve in series [[Image:]]

Q. 7.Solve in series [[Image:]]

Q. 8.Solve in series [[Image:]]

Q. 9.Solve in series [[Image:]]

Q. 10.Solve in series [[Image:]]

Q. 11.Solve in series [[Image:]]

Q. 12.Solve in series [[Image:]]

Q. 13.Solve in series [[Image:]]

Q. 14.Transform the equation [[Image:]],

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 =nP_n+(2n-3)P_n-2+(2n-7)P_n-4+………..

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

Q. 18.Show that [[Image:]]

Q. 19.Prove that [[Image:]]

Q. 20.Prove that [[Image:]]