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test1_Solution

# test1_Solution - Math 242 Spring 2011 Test 1 Name.f'tltp...

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= S d,d* \ *-'dx = S o'u -u (x) -rJ Q.dt= (.t . o\ Math 242, Spring 2011 Test 1 Name:.f ?.(.'tltp/ .... 1. (20 points) Find a function y(r) satisfying the initial value problem: ! a'@) : -# Iv(t) :7 Check your work by verifying that your answer satisfies both the differential equation and the initial condition. )dr 4 = !(r) = C= f-( +isi1 =t{* l"Js',,{ oo"}^'Atw : L+ c I -v 5'('(\ = \tt) : t-' =+ = -t.x-tt O : -*- /

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) satisfying the initiai value ) atisfies both the differential (g rlx = 'S^r'lK, J !t+' ,._-- ^*- = frx\tune,l t 'r7t-il* 2. (20 points) Find EXPLICITLY a function gr(r problem: I 3ay' : 2rt/3(y2 + | \ Y(o) : -3 Check your work by verifying that your answer s equation and the initial condition. Se4anub{t , tt t' __ g_xYt | 3 !L+ I rt,or t\r# = KLt c, ut 7J J'tl {/, I , i\ ry )t,t 0^\ nr o^ \,n\ -(xr,r*.) \tt\= e- = g" \:'r r\ = Lrer'u , ufu ct = e"' o s-*\= ,rd''t >J'r.r.e -yz+{>o ke' Ja = crgxt"- | l/t)'€ ,14- i, , #*t an1"'4 *' : Gr)t = cueo'I CJ= 1+l= to st*wd'u-\ .lL-,,2 .{ __ J YLo\ tfo)= fl aT--l lyr i+-' *{- tg-fu a+o^ "g! \$'tf.'rd gx"t* | Ckt",. 3r!'= r( @)( t,6' 6 "^''l tsx\'\' = )D xu g'r't v Ar,, tri,\ = rxve. Qon^"? u\ = pzxY'{"o n
3. (20 points) Find a function y(r) satisfying the initial value problem: I 3*Y'-Y : L2r \Y(t) :4 Check your work by verifying that your

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test1_Solution - Math 242 Spring 2011 Test 1 Name.f'tltp...

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