Diff Eq help

[Treadstone]

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

[Treadstone]

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

[bloodhound]

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

[bloodhound]

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

[Treadstone]

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?

[Treadstone]

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?

[bloodhound]

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

[bloodhound]

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

[bloodhound]

derivative of x'/2 wrt t is just x''/2

[bloodhound]

derivative of x'/2 wrt t is just x''/2

[Treadstone]

thanks bro, that was really helpful

[Treadstone]

thanks bro, that was really helpful

[bloodhound]

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

[bloodhound]

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

[MandrakeRoot]

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

[MandrakeRoot]

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