HW-3_solutions

HW-3_solutions - HW-3 SOLUTIONSec 2.22. No3. Yes6. Yes8. We...

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Unformatted text preview: HW-3 SOLUTIONSec 2.22. No3. Yes6. Yes8. We separate the variables and rewrite the equation in the form:31y dydxx=.Integrating both sides, we have:31y dydxx=,41ln4yxC=+.Then, solving the last equation for ywe obtain: 141(4ln)yxC=+, where 14CC=.9. We separate the variables and rewrite the equation in the form:1(2sin )dyx dxy=+.Integrating both sides, we have: 1(2sin )dyx dxy=+,ln2cosyxxC=-+.Then, solving the last equation for ywe obtain: 2cos1xxyC e-=, where 1CCe=.10. We separate the variables and rewrite the equation in the form:213dxt dtx=.Integrating both sides, we have: 213dxt dtx=,311ln33xtC=+.Then, solving the last equation for xwe obtain: 31txC e=, where 31CCe=.11. We separate the variables and rewrite the equation in the form:2222111cossec11dydxydydxyxx==++.Integrating both sides, we have: 21cos 2121ydydxx+=+,11sin 2arctan24yyxC+=+.This is an implicit solution.20. We separate the variables and rewrite the equation in the form:2(21)(342)ydyxxdx+=++.Integrating both sides, we have: 2(21)(342)ydyxxdx+=++,23222yyxxxC+=+++.Then, solving the last equation for ywe obtain: 321( 114884)2yxxxC=-++++.Substitution of x=and (0)1y= -yields: 1142C-+= -,141C+=, (141C+= -doesn’t make sense.)Hence,C=and321(11488 )2yxxx= -++++.21. We separate the variables and rewrite the equation in the form:1cos21dyxdxy=+.Integrating both sides, we have: 1cos21dyxdxy=+,1sinyxC+=+.Then, solving the last equation for ywe obtain: 22sin2sin1yxCxC=++-.Substitution of xπ=and ( )yπ=yields: 21C=-.We have to take 1C=so that 1y+. Then, the solution is2sin2sinyxx=+....
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This homework help was uploaded on 04/16/2008 for the course MA 341 taught by Professor Schecter during the Spring '08 term at N.C. State.

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HW-3_solutions - HW-3 SOLUTIONSec 2.22. No3. Yes6. Yes8. We...

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