Question

1. [-75 Points] DETAILS LARCALCET7 5.1.044. MY NOTES ASK Find the particular solution of the differential equation that satisfies the initial condition(s). (Remember to use absolute values where appropriate.) 5 f"(x) x2 f'(1) = 6, f(1) = 5 = f(x) = Submit Answer

Answer 1

* or 2 x OV 5 22 Integration We have c be the constant OV, 으 of integration Given that f* (x) = 3 - 2 or a {f'cas} d {f'cals da both sides d{f'(x)} = 5 4 dx f'(x) = -5 te given that! f(a)=6 Putting x=1 We have: f'(a)=-5te 6=- ca 11 elcas or a { fcal} = -5 + 11 then or, 5 te Thus 5 2 + 11

[o be the last or, Or, d {f(a)} (-5 tat) da Integrating both sides we have a sd $CQ Se stad) da 8 (༡༥) -5 Inlaltida +D given that $CA) = 5 Putting then we have fcl) =-5 lnldlt ldolt D OY 5 - -o tld or -6 D be the constant of intedration = a=1 +D D

nusi & cao --5 ln lalt 11a -6 Hence, eca - sin(x) +112-6