Quiz 2 Solved - Partial Differential Equations - Spring 2009 | MTH 3326, Quizzes of Differential Equations

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Math 3326 Quiz #2 SPRING SEMESTER 2009 Name ___ SOLUTIONS 1. Find the general solution to the first-order PDE Uz + yuy — u = 0. In your solution, identify and solve the characteristic equation and the transformed equation in order to solve the above PDE. CE: aa “4 => oly = dx > Any ax R a + y= a Cex 8c Aake YOK. y)= Ae * 2 Sip yats tey the chavacternsthe cunts are the expmentals yaCeX whee C8 an cwbirhaug Constant. Tgtee tn -w=0 _ . Mecca ke o Its os . le “Ws =o oe ews Hq) 80 wee *t4) fe the general eieahie on 20 is Um y)= & *$ (ye, 2, Now solve, if possible, the above first-order equation with Cauchy data u(z,y) = 2 on y = 3e™. Aye Want: J= u&,3e&)= e€ (Be. e*) = e “£G) This tee IS ngs So ttug Cauchy poblen faa ne selvcfi 3. Now solve, if possible, the same first-order equation but this time with Cauchy data u(z,y) = e® on the curve y = e*. Yiw, we Want; e%= Ulx,e%)= eX $leX%. > ef) ae In thas Caag, there ave unfini j Setvdions te aa tire Cam hg peblems specifically SUK, y= € “Pye roy Avhore fis an abi olifferent able Sanchne ahebng a 7e/ fb )= £ $y) =e I= costt-1) ete.