Answer Happy

Note: This assignment is worth 4% of your total marks 4.1 Exercises Q1: a) Verify that the given two-parameter family of functions is the general solution of the differential equation. b) Find a member of the family that is a solution of the initial value problem y=ce²¹ +₂ ¹. (-0, 0); y-y-0, y(0)-0, y(0)-1 Q2: Determine whether the given set of functions is linearly independent. 1- 2- f(x)=e¹, fix)=². xx, f(x)=x².50-4x-3² 4.2 Exercises Q3) The indicated function vik) is a solution of the given differential equation. Use reduction of order, to find a second solution v 1- 2- 3- xy-7xy+16y=0; y-x¹ "-y-6y=0 4- y" + 16y=0, 4.3 Exercises Q4: Find the general solution of the given differential equation. 1. 2- 3- Q5: Solve the given initial-value problem. 1- 2- S- y" - 36y=0 3- y+2y+y=0: y=xe 4x²y"+y=0: ₁x¹/2 lnx + 8y + 16y=0 y"+16y=0, y(0)=2. y'(0) = -2 y-2y+y=0. y(0) 5. y'(0) = 10 4- y" + 3y + 2y=6 3. y"-2y + 5y e sinx y"+y+2y=0, y(0)=y'(0) = 0 b) Solun the men initial value problem -4y + 5y = 0 4.4 Exercises Q6) Solve the given differential equation by undetermined coefficients 1- 2- y"+ 2y = 2x+5-e-20 4 by y=x2 day de +y=0,