Treadstone Posted November 19, 2004 Share Posted November 19, 2004 if anyone is on and able to check my work on these couple diff eqs i would really appreciate it. The prof doesnt assign problems with solutions so i cant ever check my work . That is frustrating....heres a couple x' = 3x - 2y + sin(t) y' = 4x - y - cos(t) i used the differential operator and the method of undetermined coeffcients to get this answer..dont think its right because its so ugly x = [e^(t)] * [Acos(2t) + Bsin(2t)] - (1/10)sin(t) + (7/10)cos(t) y = [Ce^(t)] * [Dcos(2t) + Esin(2t)] + (11/10)sin(t) + (3/10)cos(t) And, if you are up to it, heres another one...D is the differential operator (D-3)[x] + (D-1)[y] = t (D+1)[x] + (D+4)[y] = 1 got answers useing the same method as above... y = Ae^(11t) + (1/10)t + (3/11) x = Be^(3t) - (9/20)t + (19/330) Thanks for anyone who responds...anyone going to IUP should avoid Dr. Kuo, lol, check her rating on http://www.ratemyproffesor.com and i've had her for 4 classes, she is terrible...my only Cs in math Link to comment Share on other sites More sharing options...
Treadstone Posted November 19, 2004 Author Share Posted November 19, 2004 if anyone is on and able to check my work on these couple diff eqs i would really appreciate it. The prof doesnt assign problems with solutions so i cant ever check my work . That is frustrating....heres a couple x' = 3x - 2y + sin(t) y' = 4x - y - cos(t) i used the differential operator and the method of undetermined coeffcients to get this answer..dont think its right because its so ugly x = [e^(t)] * [Acos(2t) + Bsin(2t)] - (1/10)sin(t) + (7/10)cos(t) y = [Ce^(t)] * [Dcos(2t) + Esin(2t)] + (11/10)sin(t) + (3/10)cos(t) And, if you are up to it, heres another one...D is the differential operator (D-3)[x] + (D-1)[y] = t (D+1)[x] + (D+4)[y] = 1 got answers useing the same method as above... y = Ae^(11t) + (1/10)t + (3/11) x = Be^(3t) - (9/20)t + (19/330) Thanks for anyone who responds...anyone going to IUP should avoid Dr. Kuo, lol, check her rating on http://www.ratemyproffesor.com and i've had her for 4 classes, she is terrible...my only Cs in math Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 i couldnt be bothered to do it myself. but i just banged the problem into maple and here are the sultions. the for the first [math]y(t)=e^{t}(B\sin(2t) + A\cos(2t))+\frac{7}{10}\sin(t)+\frac{11}{10}\cos(t)[/math] [math]x(t)=\frac{e^{t}}{2}(B\sin(2t)+B\cos(2t)+A\cos(2t)-A\sin(2t))+\frac{7}{10}\cos(t)-\frac{1}{10}\sin(t)[/math] note: A and B are same constants in x andy since the two diff equations are coupled. edit: why isnt x(t) showing up properly? anyway, i am sure you can understand the solution from the latex Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 i couldnt be bothered to do it myself. but i just banged the problem into maple and here are the sultions. the for the first [math]y(t)=e^{t}(B\sin(2t) + A\cos(2t))+\frac{7}{10}\sin(t)+\frac{11}{10}\cos(t)[/math] [math]x(t)=\frac{e^{t}}{2}(B\sin(2t)+B\cos(2t)+A\cos(2t)-A\sin(2t))+\frac{7}{10}\cos(t)-\frac{1}{10}\sin(t)[/math] note: A and B are same constants in x andy since the two diff equations are coupled. edit: why isnt x(t) showing up properly? anyway, i am sure you can understand the solution from the latex Link to comment Share on other sites More sharing options...
Treadstone Posted November 19, 2004 Author Share Posted November 19, 2004 thanks a lot man, that realy helped me out, good to see i'm on the right track....did you happen to maple the 2nd one? Also, i'm getting screwed up on something else, same section, but i dont remember if the derivative of x'/2 is x''/2 or x''...any help there? Link to comment Share on other sites More sharing options...
Treadstone Posted November 19, 2004 Author Share Posted November 19, 2004 thanks a lot man, that realy helped me out, good to see i'm on the right track....did you happen to maple the 2nd one? Also, i'm getting screwed up on something else, same section, but i dont remember if the derivative of x'/2 is x''/2 or x''...any help there? Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 for the second one i got from maple [math]x(t)=-\frac{26}{121}-\frac{4}{11}t+Ae^{11t}[/math] [math]y(t)=\frac{45}{121}-\frac{1}{11}t-\frac{4}{5}Ae^{11t}[/math] note again A is same in x and y Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 for the second one i got from maple [math]x(t)=-\frac{26}{121}-\frac{4}{11}t+Ae^{11t}[/math] [math]y(t)=\frac{45}{121}-\frac{1}{11}t-\frac{4}{5}Ae^{11t}[/math] note again A is same in x and y Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 derivative of x'/2 wrt t is just x''/2 Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 derivative of x'/2 wrt t is just x''/2 Link to comment Share on other sites More sharing options...
Treadstone Posted November 19, 2004 Author Share Posted November 19, 2004 thanks bro, that was really helpful Link to comment Share on other sites More sharing options...
Treadstone Posted November 19, 2004 Author Share Posted November 19, 2004 thanks bro, that was really helpful Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 I am currently doing the first one by hand... tell you the result later. seem to get a wrong complementary function... anyway ill try it later again. its 3.43 am. have to get up at 7:30 for lectures Link to comment Share on other sites More sharing options...
bloodhound Posted November 19, 2004 Share Posted November 19, 2004 I am currently doing the first one by hand... tell you the result later. seem to get a wrong complementary function... anyway ill try it later again. its 3.43 am. have to get up at 7:30 for lectures Link to comment Share on other sites More sharing options...
MandrakeRoot Posted November 19, 2004 Share Posted November 19, 2004 if anyone is on and able to check my work on these couple diff eqs i would really appreciate it. The prof doesnt assign problems with solutions so i cant ever check my work . That is frustrating....heres a couple x' = 3x - 2y + sin(t) y' = 4x - y - cos(t) i used the differential operator and the method of undetermined coeffcients to get this answer..dont think its right because its so ugly x = [e^(t)] * [Acos(2t) + Bsin(2t)] - (1/10)sin(t) + (7/10)cos(t) y = [Ce^(t)] * [Dcos(2t) + Esin(2t)] + (11/10)sin(t) + (3/10)cos(t) And' date=' if you are up to it, heres another one...D is the differential operator (D-3)[x'] + (D-1)[y] = t (D+1)[x] + (D+4)[y] = 1 got answers useing the same method as above... y = Ae^(11t) + (1/10)t + (3/11) x = Be^(3t) - (9/20)t + (19/330) Thanks for anyone who responds...anyone going to IUP should avoid Dr. Kuo, lol, check her rating on http://www.ratemyproffesor.com and i've had her for 4 classes, she is terrible...my only Cs in math Your solutions of Diff.eq.'s are always easy to verify ! Try taking the appropriate derivatives and see if they actually satisfy your DE ! If that is the case you have indeed found a solution (maybe not all but well....), if they dont satisfy your DE then you havent found a solution. So with this type of exercise you should be able to check your answers properly. Mandrake Link to comment Share on other sites More sharing options...
MandrakeRoot Posted November 19, 2004 Share Posted November 19, 2004 if anyone is on and able to check my work on these couple diff eqs i would really appreciate it. The prof doesnt assign problems with solutions so i cant ever check my work . That is frustrating....heres a couple x' = 3x - 2y + sin(t) y' = 4x - y - cos(t) i used the differential operator and the method of undetermined coeffcients to get this answer..dont think its right because its so ugly x = [e^(t)] * [Acos(2t) + Bsin(2t)] - (1/10)sin(t) + (7/10)cos(t) y = [Ce^(t)] * [Dcos(2t) + Esin(2t)] + (11/10)sin(t) + (3/10)cos(t) And' date=' if you are up to it, heres another one...D is the differential operator (D-3)[x'] + (D-1)[y] = t (D+1)[x] + (D+4)[y] = 1 got answers useing the same method as above... y = Ae^(11t) + (1/10)t + (3/11) x = Be^(3t) - (9/20)t + (19/330) Thanks for anyone who responds...anyone going to IUP should avoid Dr. Kuo, lol, check her rating on http://www.ratemyproffesor.com and i've had her for 4 classes, she is terrible...my only Cs in math Your solutions of Diff.eq.'s are always easy to verify ! Try taking the appropriate derivatives and see if they actually satisfy your DE ! If that is the case you have indeed found a solution (maybe not all but well....), if they dont satisfy your DE then you havent found a solution. So with this type of exercise you should be able to check your answers properly. Mandrake Link to comment Share on other sites More sharing options...
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