Question

Question 4 Solve the differential equation. 2xy' + y = 2V*

Answer 1

14) solution Given differential equation is 2xy'+y = 2 va Dividing on both side with ſal", we get y't my = on tehnyt -(0) Equation © jo linear in "y" where pcd) = ha and Qata Integrating factor is I. F = esp da I.F = edžada - Ina zelnal I. F ayz The general solution to given diffuntial equation is y(I.F)- JQ.I.F dx+c yoxlk2 - ) F alz dute

y. Ta = fax tc y va = a + c y = a (a + c) y = a + c. all (5 solution Given dififerential equation is ay'+y = almal Dividing on both side with "X" 1. y' + 2 y = lnx do + 5y = Inc - 0 Equation © js lineas in "y" where pa and Qua) - Ina Integrating factor is I.F=eJpda eht da elna za =

The general solution of the given differential equation is Y (IF ) - Q.I.F 18+ Y.x = [X \na da +c 2y = [int]x dx. - Strony" ) in da de ]+c ay box - Ja der] +c = 1nx - fade +c = 1 + 1*2)+c se Inx - y s plna - + - © given initial condition is y(1) =0 200 90) = lp1) - + = 0 f(0) = 4 +C =0 c=1/4

put the value of c in equation@ 19 = 4 Ina - pop + 42 (7) solution - Given that a = tet and y=t+Sint di = (tet) = ct et 4 tiety's letztet og (t +siot) = + cost Now dy dh x de da = (1+cost ) x 1 It cost da et (1+t) 8) solution - The para matric curves are a = tant and y=$?+++

dt = (t2-1) = 27-1 (+2+7 + 1) = 2t + dy = 27+) da att c..' where t=1) day cut Co, 3) is m = 2015+) = 3 = 3 20171 The equation of the tangent line to the given curve at (0, 3) is Y-3 = 3 (8-0) Curve 9-3 = 32 Y = 3x +3 lis a regulised equation