@Waqas - Ah those self-destructive delaying tactics. Its just an ordinary preparation going on. I ve not touched compulsories. But not afraid of English precise or essay either.

I am doing ODEs. I found the vector portion interesting - the surface area and volume plus few theorms. Plus on and off cursory looks to physics with hopes that a one time thorough brushing up of the concepts will revive the dormant knowledge.

I think i can handle EDS and Islamiat. Current affairs is daunting but i hope i can pass that :). Overall, not the bookwormish type of studies for CSS, but at times, for few moments, i feel the pressure that culminates in a genial consolation.

[quote] (x^2+1)y''+xy'-y=0 came in CE-2014 paper. [/quote]

It is a question of power series method.

[quote] (x^2+1)y''+xy'-y=0 came in CE-2014 paper. [/quote]

It is a question of power series method.
secondly i recently appeared in MA part I, so Economics is already prepared, because Part I of Economics is enough for CSS. Last year there were two numericals in Economics paper so Economics has suddenly become a scoring subject

[quote]Ah those self-destructive delaying tactics.[/quote] really? then i am already on self destruct :). [quote] Its just an ordinary preparation going on.[/quote] thanks for saying that.

good luck to both

[B]attempt one question of physics from past papers everyday on paper and note your time[/B]

for essay and G.K. listen to one lecture of world history everyday from the following site:
[url]http://www.pearlandisd.org/webpages/gjohnson/ap_world.cfm?subpage=47199[/url]

the following is in my opinion the best book on Physics:
[url]http://dl.bookzz.org/genesis/563000/214014c3bdba66396fc33acd97dc9c9b/_as/%5BRaymond_A._Serway,_John_W._Jewett%5D_Physics_for_Sc(BookZZ.org).pdf[/url]

[QUOTE=waqas izhar;746809][B]attempt one question of physics from past papers everyday on paper and note your time[/B]

for essay and G.K. listen to one lecture of world history everyday from the following site:
[url]http://www.pearlandisd.org/webpages/gjohnson/ap_world.cfm?subpage=47199[/url]

the following is in my opinion the best book on Physics:
[url]http://dl.bookzz.org/genesis/563000/214014c3bdba66396fc33acd97dc9c9b/_as/%5BRaymond_A._Serway,_John_W._Jewett%5D_Physics_for_Sc(BookZZ.org).pdf[/url][/QUOTE]

Brother how one can opt for a method which is not being asked in the exam?
In previous papers, they clearly asked that solve the following differential eq. using power series method but this time no such statement was given. And let say if u start attempting it with the power series method, what would be your initial center of the series i,e xo??????? Normally it should be given if he wants us to attempt it with power series.............
Another important that i is in my mind is that when i went through the last paper, i found some of the question in which they had asked to find recurrence relation & power series solution of the given differential equation.
What is the recurrence relation????????

[QUOTE](x^2+1)y''+xy'-y=0 came in CE-2014 paper. [/QUOTE]

[QUOTE=waqas izhar;746801]It is a question of power series method.[/QUOTE]

Isn't it a second order Cauchy Euler Equation?


[QUOTE=engr sarakhan;746928]Brother how one can opt for a method which is not being asked in the exam?
In previous papers, they clearly asked that solve the following differential eq. using power series method but this time no such statement was given. And let say if u start attempting it with the power series method, what would be your initial center of the series i,e xo??????? Normally it should be given if he wants us to attempt it with power series.............
Another important that i is in my mind is that when i went through the last paper, i found some of the question in which they had asked to find recurrence relation & power series solution of the given differential equation.
What is the recurrence relation????????[/QUOTE]


When there is no mention of any method in the question, the choice is yours. Use any suitable method to reach the solution. And sometimes only one method is applicable to a question.

List down all possible methods of solving all kinds of DEs or PDEs. Things would be much easier.


P.S. avoid Netspeak.

@Gotam
I do not think it is a cauchy Euler Equation. As the standard form of 2nd order Cauchy Euler Equation is x2y''+axy'+by=0 or r(x). Can we convert the above equation into this standard form by any means? I think solving it by power series is the way we are left with.

For

(x^2+1)y''+xy'-y=0

and recurrence relation go through following links.

[url]http://www.math.ualberta.ca/~xinweiyu/334.1.10f/DE_series_sol.pdf[/url]

[url]http://www.math.buffalo.edu/~asikora/epch8.pdf[/url]

[QUOTE=engr sarakhan;746945]@Gotam
I do not think it is a cauchy Euler Equation. As the standard form of 2nd order Cauchy Euler Equation is x2y''+axy'+by=0 or r(x). Can we convert the above equation into this standard form by any means? I think solving it by power series is the way we are left with.[/QUOTE]


Yes, it is a power series question :)

This is Q-7 in the exercise given on page: (solve it and verify the answer)

[url]http://www.stewartcalculus.com/data/CALCULUS%20Concepts%20and%20Contexts/upfiles/3c3-UseSeries-SolveDEs_Stu.pdf[/url]

Here is another dilemma.................
In CE-2014 the following question was asked.
dy/dx = 1/(x+y^2) Can any one classify this equation? Which method does suit it?
It is none of the following, Seperable, homogeneous, exact. Neither can we write it in first order diff Eq stand form. i.e y'+p(x)y=q(x), nor it is a bernollie eq.
If we expand it we get
(x+y^2)dy=dx
Kindly help me in solving it.