Can Alfonso Overcome His Differential Equations Challenges at Texas Tech?

[Alfonso]

Howdy!

A little introduction, my name is Alfonso, I'm a Physics major. I'm orginally from Mexico but I've been living in the States for about half my life. I'm beginning my third year of college at Texas Tech and am thoroughly enjoying my time here! I'm actually a bit behind on my classes because I was transferred late and missed two days of school. This actually led me to my debut here! (I don't know if that's a good thing yet) My professor kindly lended my $200 to purchase my Differential Equations book for ODE about half an hour ago. I've been struggling with this homework. So far I've shot three problems down but the rest of these (posted) are perplexing me. I was wondering if I could get some help? I look forward to contributing in the future! =D


Problem #1
Find the position http://webwork.math.ttu.edu/wwtmp/equations/aa/8727e53c828c4d86d5c60edbbf40ec1.png of a moving particle with the given acceleration http://webwork.math.ttu.edu/wwtmp/equations/72/ac5d7e539f91d520f21d357bcf7e5e1.png , initial position http://webwork.math.ttu.edu/wwtmp/equations/ad/4899084e580a79133cf44eded9da561.png , and initial velocity http://webwork.math.ttu.edu/wwtmp/equations/0c/e42c79e45f5ab6a87cc4927b0ea3831.png

http://webwork.math.ttu.edu/wwtmp/equations/57/449da94945160e834abdaeaa07482b1.png .

http://webwork.math.ttu.edu/wwtmp/equations/ed/055d3c2feee89d38e7a107e1f9295f1.png ____

Problem #2
The general solution to http://webwork.math.ttu.edu/wwtmp/equations/0d/9aa457ffd2e5fd57019eb3dc9509db1.png can be written in the form http://webwork.math.ttu.edu/wwtmp/equations/ee/e1587a9f2447ef060c9bcee0b50a3d1.png where [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8f/ef7df1811915931ddec43c23ba91971.png is an arbitrary constant.

[PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8b/0b3b5b8f0003a2d7dd6750d2846db31.png ____ For this problem I keep getting ln |y| = 3 ln |2+x| +C Is this correct? Am I missing a step?

Problem #4
The solution to http://webwork.math.ttu.edu/wwtmp/equations/07/c2f63eb85fff45d596ccdb23d6a5f51.png with http://webwork.math.ttu.edu/wwtmp/equations/7d/c4d9a585631fc66949ef3e54457c291.png is

[PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/ea/e6cfcd8bc239c880ec11f7a55587d41.png ____ For this problem I get y = square root of 2e^x +C is this correct?

Problem #5
The general solution of the first order linear equation http://webwork.math.ttu.edu/wwtmp/equations/ba/acc22b431c3dd54785050bbe4867de1.png can be written as http://webwork.math.ttu.edu/wwtmp/equations/b7/275c75cc14d44935210377b1fba0731.png where [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8f/ef7df1811915931ddec43c23ba91971.png is an arbitrary constant.

[PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8b/0b3b5b8f0003a2d7dd6750d2846db31.png ____
Problem #6
Solve the first order linear Initial value problem http://webwork.math.ttu.edu/wwtmp/equations/e9/eeb16dc4391cbd863fb98e7663f5111.png with http://webwork.math.ttu.edu/wwtmp/equations/9f/d213edbcefb8312bf794d53d179c6b1.png .

[PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/ea/e6cfcd8bc239c880ec11f7a55587d41.png ____
Problem #7
Solve the first order linear Initial value problem http://webwork.math.ttu.edu/wwtmp/equations/79/578d76f7f8c2e0e712da65fb7c14381.png with http://webwork.math.ttu.edu/wwtmp/equations/02/802f8b8b73ddcb133bd57d177493b11.png .

[PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/ea/e6cfcd8bc239c880ec11f7a55587d41.png ____

Problem #8
Solve the equation http://webwork.math.ttu.edu/wwtmp/equations/ea/d19b5c803d270b9885f88e186529bd1.png by first setting http://webwork.math.ttu.edu/wwtmp/equations/5a/aba0fdb4dd187e8f983082d943229b1.png to obtain a first order equation for [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/a7/34522e64f905980d2440692bdd1a1a1.png . After you solve for [PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/a7/34522e64f905980d2440692bdd1a1a1.png recall that http://webwork.math.ttu.edu/wwtmp/equations/fc/8dfa85b8f83a506b31b726dbff5c001.png and solve the resulting pure time equation for http://webwork.math.ttu.edu/wwtmp/equations/85/067ce783e2f89ced535d722b824af51.png .

The solution can be written as http://webwork.math.ttu.edu/wwtmp/equations/be/2ae53f79b69e6792e63a0850709f691.png where http://webwork.math.ttu.edu/wwtmp/equations/4c/9829f8d94c26e0c1df882bc622fafd1.png and http://webwork.math.ttu.edu/wwtmp/equations/b8/f60b6af1267d2e64128ce6f0c84c8c1.png are arbitrary constants.

[PLAIN]http://webwork.math.ttu.edu/wwtmp/equations/8b/0b3b5b8f0003a2d7dd6750d2846db31.png ____

 

[rock.freak667]

For 1) v= ∫ a(t) dt and s=∫v(t)dt

2) write your constant C as lnC instead and use nlog_ab=log_ab[ⁿ.

4) Your general solution is correct but you were given that y(0)=1, so you need to use this to find a particular solution.

5) Read http://en.wikipedia.org/wiki/Integrating_factor"

6,7) Same as #5

8)If v=y' then what is y'' equal to (in terms of v)? Now put those into the ODE and you'll get a first order equation that can be easily solved.