Differential Equation BS 3 Semester/Term UOS — University of Sargodha 2018

University of Sargodha

BS 3rd Term Examination 2018

Subject: Computer Science Paper: Differential Equation (CMP:2215)

Time Allowed: 2:30 Hour

Maximum Marks: 80

Objective Part (Compulsory)

Q.1. Write short answers of the following in 2-3 lines each. (2*16)

(i) Write the normal form od the differential equation F(x,y,y',...,y(n)).

(ii) Define linear differential equation also write its standard form.

(iii) Define separable equation.

(iv) Solve the differential equation dy/dx - 3y =

6.

(v) Determine whether the differential equation (x - y^3 + y^2 sin(x))dx = (3xy^2 + 2y cos(x)dy) is exact or not.

(vi) Define initial and boundary value problems.

(vii) When y = e^3x and y = e^-3x are two independent solutions of differential equation y'' - 9y = 0, then find the general solution of given differential equation.

(viii) Define integrating factor to solve a non-exact differential equation.

(ix) Find general solution of y''' - 3y' + 2y =

0.

(x) Find the integrating factor for which the differential equation xydx + (2x^2 + 3y^2 - 20)dy = 0 is exact.

(xi) What is a Mathematical model.

(xii) Define interval of convergence.

(xiii) Show that the function f(x,y) = x^3 + y^3 is homogeneous function of degree

3.

(xiv) Find wronskian for the functions f1(x) = e^3x, f2(x) = e^-3x.

(xv) State Frobenius theorem.

(xvi) Define regular singular point of a differential equation.

visit website: ustani.pk