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Advanced Math/partial differentiation

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Expert: Robi Bhattacharjee - 7/14/2009


Question
If ycosx= e( to the power x), show that

d2y/dx2 - 2 tan dy/dx - 2y=0

i tried to work it out and i never really got to it!!

Answer
Hi Joseph

ycosx = e^x

so use implicit differentiation to find dy/dx.

So dy/dx*cosx - ysinx = e^x

So dy/dx = (ysinx + e^x)/cosx

which = (tanxe^x + e^x)/cosx

from here, just take the derivative of the above expression to get d2y/dx2. Then, plug all the values in and your problem will be solved.


Robi

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Robi Bhattacharjee

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I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

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I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

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I am in the San Diego Math Circle

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I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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