Question

(20 points) Use ONE of the following reference words for the given differential equations to indicate the methods you would you use when asked to solve the given different equations. Use N/A only if you believe the other methods are not working. Do not solve the equations. 1. Reference words: Exact Linear first order (integrating factor method) Separable 2nd order constant coefficient homogeneous (characteristic equation) Simple integration Introducing new functions (to reduce the problem to a simpler problem) N/A to indicate that none of the above methods work Note that y is short for y(t) ty'=y2 ty'= 1 = t y"+2y'=t y'+2y t (9t2+y-1)-(4y-t)y'0 y" +2y' +y t y"+2y'+y0 y" + 2y'y=0 y"+y 0

Answer 1

dy dt (t ヒ d d1dt is Simbl tegrata 3 imes integration We do a integrating tarhr etad) Sadt at gisiear First order tegraing fator

atty)-1- )Y= gt is ex act m 9t+ 9-) N t- tis N/A at i orde contaut Loctficient homogevea haracteristic eguet in) T Uharateristic euotian s tartl=0 (Yayy=0 St is nJA gnorder constaut LoefHLieut hamogeveovs