Question

on someone Hele Me Sim x nts/504579395186777014 + (graded) Section 2.6: Exact Equations and Integrating Factors < Previous Consider the differential equation: 9 + (4y sec(8y) - 8-tan(87)) y = 2 a. This equation is not exact because M, = does not equal N. b. Find an integrating factor, j, to make the equation exact. Do not include an arbitrary constant in your answer for By assuming that is a function of only (enter x or y), we get that w = c. Using the integrating factor, we get that the general solution is px,y) = a = c. Submit answer Answers - /0.6 -10.6 Instructions A C a search or type URL 0 T 4 }

Answer 1

9894+ (47° sec (89) 888 tan (M)) y' = 0 9497+ (vy®4 sec(y) - sea tan ()) dy = 0 (9 092) de + (uyºse (cy) - Sporten ley)) dy = 0 OM M(x,y) de + N(2,4) dy = 0 1 M(, ) = qe9%, 0(x,y) = 4y®sec (89) -8e" *tas (84) eng - by (782) = 0 = 2 (° 9° sec(ny) - 8ę"tan(sy)) e 10.-72 e'tan (84)) = -7e **tan (84) an эх 92 -72 e 2x The guven differential equation is not exact. ƏM AN 1. ax =-72 e tan (84) an 2M G r y fan of*unto) -] Los com = -8 tan(89) = 14) . L is a function of y only,

5-8 tan (14) dy = e Integrating factor (26) = I Jy) dy *). *(-An(n.es) en Casey) ( 2.7) = cosay 7 a is a function of [y], [u= If = cos sy multiply the integrating femes , di pberential equation. cos (By) [qe me dx + (uyʻsec (04) - 8e attan (89) ay] =0 [ qe "cus (@y) dx + (4y? 8e94 sin (y)) dy = 0 Now the given differential equation becomes exact Day by (re"*cos()) = -72e" thin lay) the one (é "sin cy)) = -72 € 9% jim (89) solution : Smx.g) dk + s (no containing tema) without x) dy = c/ Y = constant Scaletas (es) dx + 5 (499) dy = c. Ya constant

qe la cas (8+ ugoza en relas (BY+y"= solution - 7 y Cany) = ( 4 cos (89) + yu 92 in !.