MATH 202 Midterm, Spring 2005

Math 202 Mid- EXAMINATION Nahlus & Yamani Time: 75 minutes Date: April 6, 2005 Name oo ee LO Sec. 9 (12:30 Th, Yamani) Sec. 10 (2:00 Th, Yamani) Sec. 11 (9:30 Th, Nahlus), Sec.12 (2:00 Th, Nahlus) Circle Your Section Number Problems Grade Maximum Lo eee. 14 ) Terre 14 <r 14 4 oe 14 Sete 12 6 eee 12 Tab oo... 10 8ab oo... 10 Total 100 2 1) SolvetheIVP problem (x’?+1)yy'=e ” — where y(1)=0 2) Solve the BemoulliDE x’ y'-xp+y’ =0 3) Find an integrating factor to make the following DE exact. Then solve it. 2xpdx+(4x’ +6y’ +4)dy=0. 2x 4) Find the general solution of the DE y''-4y = 20x+e 5) Use the formula for Reduction of order to find the general solution of the DE (+x? py -2xy'+2y=0 giventhat y, =x isa solution 6) Find the general solution of the DE yl +3y'+2y = sine* 7a) (7 pts) Find the general solution of the DE (by any method) xy +xy'ty=0 7b) (JUST 3 pts) Use the substitution x = e’ (SHOW ALL DETAILS) to change your DE to a DE with constant coefficients. THEN STOP! STOP xy" —xy'+y=xinx THEN STOP! STOP y'tanx 8a) (7pts) Find all solutions of y= (siny' Je where Hint: Let y=Y. Then try Y=k (for some k). 8b) (JUST 3 pts) Change the following Ricatti DE to a Bernoulli DE. THEN STOP y= Py x’y’-x° (Hint: y=x isa solution) x THEN STOP