iFruit:

mathqa:

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/nonhomgeneous-differential-equations.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 non-homogeneous 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) = ((1-2π)/4) e^t cos(t/√3) - (√3(1+2π)/4) e^t sin(t/√3) - 11/4

Regards.

Thanks MathQA for volunteering your time to help solve this tough question.
Small mistake does not matter. It is just + or - of a constant value.
Overall steps posted on blog are well defined and easily followed.
But may I suggest you try to post the images of your works here. The forum does support [img] tag.

@iFruit: we need steps to understand how to solve the question, not just final answer. How to solve the problem is much more important than final answer. Appreciate if you could be more elaborate next time then :). Thanks!!!

Best regards,
Mr AMK.

justbehappy:

We have million dollar reward for sports olympics games winners, even YOG winners get tens of thousands. However, the international physics/biology/chemisty/maths/etc olympiad winners do not have such a reward system.


The local academic olympiad winners are also the tops in their own field. I feel it is really unfair that only sports olympics winners are recognised and motivated with monetary awards. Why doesn't MOE come up with a reward scheme for the academic olympiad winners?

I think the media popularity explains the difference. Sport events attract many more readers/viewers than academic events. Therefore, advertisers have to put their bucks accordingly.

It is also because sport career is risky than academic one due to early retirement age and physical injury.

mramk:

O level E-Math this year is over. Could anyone kindly share the exam paper?


Thanks.

Can anyone pls share, then I will get back with full worked solution by my son's tutor?

O level E-Math this year is over. Could anyone kindly share the exam paper?


Thanks.

Hi Parents,


Could anyone advice where to get study materials and past year exam questions for Maths Olympiad both Junior and Senior?

Thanks in advance.
Mr AMK.

Guan Hui:

Hi parents, just wondering why is there not a thread for secondary school maths questions and decided to start on one.(inspired by mathsguru contribution to this community)


So... yup this is for Q&A for secondary school maths questions.

Please state the level of the question when posting the question for the convenience of knowing which method should be used to explain the answers.(e.g. Sec 1)

Hope it helps!

Hi Guan Hui, thanks for your service. Could you please help with below question:

prove the identity: cos(x).cot(x) + sin(x) = cosec(x). (O level A-Math)

Thank alot.

worriedparent:

Original Title: Failed Maths & Science Subjects


My son has done very badly in his Sec 3 Mid-Year Exam, esp in his core subjects of E. Maths, A. Maths, Physics and Chemistry.

Can anyone help?

My son also did badly when he was in sec2. And the best decision I ever made was to hire tutors for him. After that, his attitude toward learning is more serious because he knows that I have to spend more for him. His O level result was excellent especially in Math. He credits his success toward the tutors. Now, he is in Poly and very motivated with his study.

Finding a good tutor is also very difficult. I would recommend full-time tutor, not part-time. And you need to monitor tutors as well, speak to them, ask this and that. If the tutors knows that you are watching their works, they would be more devoted.

fridayeducation:

Hello all parents,


After reading through this forum, I realised many parents are teaching their children on their own. Something my parents never had the time to do so when I were young. Therefore, as a form of encouragement to all dedicated parents. I will be providing you help with questions that you have doubts on.

You may post the questions here/PM me or email me and I will try my best to solve it at soonest and post the question/answer here so other parents who have doubts on the same type of questions may help their kids too
(but please give me a day to assist you with your questions in case i do not read my mails)

Have a great day.

Thanks for your offer. Wish to find more and more members like you in this famous forum. I will \"trouble\" you with some questions soon.
Have a nice day!