Experts are full of valuable knowledge and are ready to help with any question. Credentials confirmed by a Fortune 500 verification firm.

Get a Professional Answer

Via email, text message, or notification as you wait on our site. Ask follow up questions if you need to.

100% Satisfaction Guarantee

Rate the answer you receive.

Ask Dr Arthur Rubin Your Own Question

Dr Arthur Rubin, Doctoral Degree

Category: Calculus and Above

Satisfied Customers: 1233

Experience: Ph.D. in Mathematics, 1978, from the California Institute of Technology, over 20 published papers

Type Your Calculus and Above Question Here...

Dr Arthur Rubin is online now

Hi, here are some maths questions that need to be done with

Customer Question

Hi, here are some maths questions that need to be done with detailed working out that looks simple. There are six questions and I will upload them once there is an expert available. They are based on differential equations and sequences and series.

OK, I can do that. I should be able to upload a PDF solution in an hour or two.

Customer :

Sounds great. Thanks Arthur for helping again...

Dr Arthur Rubin :

OK, here should be a complete solution. Let me know if you need clarification or more detail. (As I'm on the Pacific coast of the US, I'm going to go to sleep shortly. I'll be back within 7 hours.)

Customer :

Hi Arthur,

Customer :

Hi Arthur,

Customer :

Hi Arthur, thanks let you know if I need clarification later when I look at it fully.

Customer :

Hi Arthur, Thanks let you know if need clarification when I look at it fully

Well, if you try substituting y = exp (t x) into the equation d^2y/dx^2 - 6 dy/dx + 10 y = 0, you get t^2 - 6t + 10 = 0, which has roots t = 3 ± i. Hence, the general solution is

y = a exp( (3+i) x) + b exp((3-i)x) = exp(3 x) ( (a+b)cos(x) + i (a-b)sin(x)).

It's the quadratic equation; the solution of a t^2 - b t + c = 0 is t = (b ± sqrt(b^2 - 4 a c))/(2 a). In this case, we get t = (6 ± sqrt(36 - 40))/2 = (6 ± sqrt(-4))/2 = (6 ± 2 i)/2 = 3 ± i.

About question 4. Which formula was used to get the sequences for question a, b and c. And if it's possible could you please give me a list of all the sequences and series formula's generally used. Thanks

For 4 (a), it was just substituting values for "n", noting sqrt(n^3) = n sqrt(n). For 4 (b), it was just substituting and adding, with no indication that there is a general formula for the partial sums, although the sum of the convergent series might be found as. For 4 (c), the usual convergent series that can be used are: sum n^-(1+ε), sum (1/(n (log n)^(1+ε))) sum(1/(n (log n) (log log n)^(1+ε))), etc.

I'm heading off again; should be back in about 3 hours, at which time I'll probably need to get some sleep.

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.

JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.

Web sites like justanswer.com/legal ...leave nothing to chance.

Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.

Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.

I will tell you that...the things you have to go through to be an Expert are quite rigorous.

What Customers are Saying:

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C.Freshfield, Liverpool, UK

Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C.Freshfield, Liverpool, UK

This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!!AlexLos Angeles, CA

Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult.GPHesperia, CA

I couldn't be more satisfied! This is the site I will always come to when I need a second opinion.JustinKernersville, NC

Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. EstherWoodstock, NY

Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. RobinElkton, Maryland

He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here.DianeDallas, TX