Hi all,
Allow me to open this humble thread to assist students who are preparing for their Alevel Maths examination.
Within my ability and time budget, I will try to response to all questions.
For clarity, questions with geometry or complex formula, let's use PNG image format for posting.
MathQA Min Tan.
MathQA tutor  Ask your Alevel Maths questions here!
Is there life after O/ALevels? Definitely! How well a person does in tertiary education is correlated with job opportunities open to the person. Discuss issues pertaining to nstitutes of higher learning here.
MathQA tutor  Ask your Alevel Maths questions here!
by mathqa » Thu Oct 28, 2010 7:43 am

mathqa  YellowBelt
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by OK Lor » Sun Oct 31, 2010 10:48 pm
Hi,
I'm not taking Alevel Maths this year, but interested to know the solution for part (b):
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
Thanks.
I'm not taking Alevel Maths this year, but interested to know the solution for part (b):
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
Thanks.

OK Lor  OrangeBelt
 Posts: 44
 Joined: Sun Apr 11, 2010 10:23 am
 Total Likes: 0
by iFruit » Tue Nov 02, 2010 10:05 pm
OK Lor wrote:Hi,
I'm not taking Alevel Maths this year, but interested to know the solution for part (b):
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
Thanks.
Hi OK Lor,
Is this Alevel question? AFAI can see, The equation is a nonhomogeneous linear differential equation, so it needs some background to understand the solution..

iFruit  BlueBelt
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by OK Lor » Tue Nov 02, 2010 10:39 pm
Hi iFruit,
This question is from Malaysia A level paper which I came across while browsing the web .
Thanks.
This question is from Malaysia A level paper which I came across while browsing the web .
Thanks.

OK Lor  OrangeBelt
 Posts: 44
 Joined: Sun Apr 11, 2010 10:23 am
 Total Likes: 0
by iFruit » Tue Nov 02, 2010 10:53 pm
OK Lor wrote:Hi iFruit,
This question is from Malaysia A level paper which I came across while browsing the web .
Thanks.
From what I understand ( the wording is not great), it is asking for a solution of the equation 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t given the initial conditions.
Let me know if you are interested, I can try and and work out a solution (need to recollect my linear diff equations first) but as I said it needs some background theory on linear diff equations first.

iFruit  BlueBelt
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by atutor2001 » Wed Nov 03, 2010 1:04 am
OK Lor wrote:Hi,
I'm not taking Alevel Maths this year, but interested to know the solution for part (b):
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
Thanks.
diff both statement wrt to t
so the first one is y'' + 2x'' =2x'
second one is y''  x'' =2y'+1
then simulataneous : statement 1 + 2 x statement 2
so we get 3y''=2x'+4y'+2
then we sub y'x'=2y+t (2nd given eqn) into it
3y'' = 2(y'2yt) +4y' +2
3y'' = 2y'4y2t+4y'+2
3y'' = 6y'4y2t+2
3y''6y'+4y =22t
Disclaimer : Above working not from me. Was chatting with my kid so took the opportunity to test

atutor2001  KiasuGrandMaster
 Posts: 1305
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by mathqa » Wed Nov 03, 2010 1:13 am
iFruit wrote:OK Lor wrote:Hi,
I'm not taking Alevel Maths this year, but interested to know the solution for part (b):
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
Thanks.
Hi OK Lor,
Is this Alevel question? AFAI can see, The equation is a nonhomogeneous linear differential equation, so it needs some background to understand the solution..
iFruit is right to point out that this question is nonhomogeneous linear differential equation. But it is nice to have for A level since it would test students's competence in many areas at once.
The solution is is posted at my blog. Cannot post it here due to oversize images.
http://mathqa.blogspot.com/2010/11/nonh ... tions.html
MathQA

mathqa  YellowBelt
 Posts: 13
 Joined: Wed Oct 27, 2010 6:43 pm
 Total Likes: 0
by OK Lor » Wed Nov 03, 2010 12:03 pm
mathqa wrote:iFruit wrote:OK Lor wrote:Hi,
I'm not taking Alevel Maths this year, but interested to know the solution for part (b):
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
Thanks.
Hi OK Lor,
Is this Alevel question? AFAI can see, The equation is a nonhomogeneous linear differential equation, so it needs some background to understand the solution..
iFruit is right to point out that this question is nonhomogeneous linear differential equation. But it is nice to have for A level since it would test students's competence in many areas at once.
The solution is is posted at my blog. Cannot post it here due to oversize images.
http://mathqa.blogspot.com/2010/11/nonh ... tions.html
MathQA
Hi,
Thanks to all the Maths Guru here

OK Lor  OrangeBelt
 Posts: 44
 Joined: Sun Apr 11, 2010 10:23 am
 Total Likes: 0
by iFruit » Wed Nov 03, 2010 8:34 pm
mathqa wrote:
If x(t) and y(t) are variables satisfying the differential equations
dy/dt + 2 dx/dt = 2x +5 and dy/dt – dx/dt = 2y + t,
(a) Show that 3 d²y/dt²  6 dy/dt + 4y = 2 – 2t.
(b) Find the solution x in terms of t for the second order of differential equation given that y(0) = y’(0) = pi.
The solution is is posted at my blog. Cannot post it here due to oversize images.
http://mathqa.blogspot.com/2010/11/nonh ... tions.html
MathQA
Hi MathQA,
Nice working. But I think there is a small mistake in it. You can't apply initial conditions to the homogeneous equation (equation 6) as they are initial conditions for nonhomogeneous equation. That's why your solution doesn't tally back for initial conditions. Also particular solution C = 11/4
The solution after applying initial conditions to the general equation should be (pi = π)
x(t) = ((12π)/4) e^t cos(t/√3)  (√3(1+2π)/4) e^t sin(t/√3)  11/4
Regards.

iFruit  BlueBelt
 Posts: 217
 Joined: Thu Sep 09, 2010 11:20 am
 Total Likes: 0
by atutor2001 » Wed Nov 03, 2010 9:48 pm
Whoa! So scary. Read so many times also no understand. I didn't know my poor kids have been subjected to such "torture". Must be nicer to them now.
So funny when comparing this to Pr Math. Parents are making so much noise when kids are in Pr but did not know what their older kids are facing.
So funny when comparing this to Pr Math. Parents are making so much noise when kids are in Pr but did not know what their older kids are facing.
Last edited by atutor2001 on Wed Nov 03, 2010 9:51 pm, edited 3 times in total.

atutor2001  KiasuGrandMaster
 Posts: 1305
 Joined: Thu Aug 27, 2009 11:08 pm
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