# 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-x^{2})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} + 9P_{9}.

Q. 16.Show that xP’_{n} =nP_{n}+(2n-3)P_{n-2}+(2n-7)P_{n-4}+………..

Q. 17.Show that 11(x^{2}-1)P’_{5} = 30 (P_{6}-P_{4}).

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

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

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