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 October 28th, 2012, 08:42 PM #1 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 My First Differential Equation Book says solve the following Differential Equation dy/dx = 8x^(3) - 9X^(2) + 4 I will try but need the forum's help dy = (8x^(3) -9x^(2) +4) dx y = 8x^(4)/(4) - 9x^(3)/(3) +4x + C Is this done?
 October 28th, 2012, 08:45 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: My First Differential Equation Almost, you just need to reduce your fractions. Good work!
 October 28th, 2012, 08:50 PM #3 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: My First Differential Equation Mark, I can do that lol I have about 15 to work through over the next day and a half Will you show me one so I can use it as a reference problem. Here is a rather simple one but I want to take note and follow step by step from start to finish how you guys do here goes... dy/dx =( x^(2) + 2x -3 ) / (x^(4))
 October 28th, 2012, 09:07 PM #4 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: My First Differential Equation We are given: $\frac{dy}{dx}=\frac{x^2+2x-3}{x^4}=x^{-2}+2x^{-3}-3x^{-4}$ Integrate with respect to x: $\int\frac{dy}{dx}\,dx=\int x^{-2}+2x^{-3}-3x^{-4}\,dx$ $y=\frac{x^{-1}}{-1}+2\frac{x^{-2}}{-2}-3\frac{x^{-3}}{-3}+C$ $y=-\frac{1}{x}-\frac{1}{x^2}+\frac{1}{x^3}+C$ $y=C-\frac{x^2+x-1}{x^3}$
 October 29th, 2012, 01:14 PM #5 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: My First Differential Equation Mark, This is a perfect for reference material. The very last step. Can you explain the Algebra to me on that one? Why did you pull the C back? Thanks like always Mark. I really appreciate being able to reference this here.
 October 29th, 2012, 03:03 PM #6 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: My First Differential Equation I dislike leading negatives, so I simply put the constant in front.
 October 29th, 2012, 07:38 PM #7 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 How come the book doesn't provide worked examples for reference?
 October 29th, 2012, 07:51 PM #8 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: My First Differential Equation Well it does skip. I am taking 2 calc classes this semester. calc1 and biz calc. The biz calc class book cost near 400. it is very nice and is used for 2 and 3 as well. The instructor does make constant comments about how the book does tell this and the book doesn't tell this. I told him tonight I was going to have to put a lot of weight on him
 October 30th, 2012, 10:44 AM #9 Global Moderator   Joined: Dec 2006 Posts: 21,026 Thanks: 2257 The basics of calculus are reasonably easy, but you need to understand elementary algebra as well.
 October 30th, 2012, 04:40 PM #10 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: My First Differential Equation I was thining about this last night in class skippy when instructor said that we were now moving into the first Fundamental Theroem of Calculus Almost 90% Algebra. If this is true, I believe many if not all Calculus students refine and grow and develop their Algebra in the Trig and Calculus 1,2&3 (if they get that far). I'll have you and Mark and anybody else on this forum know a few things: Every student in my class struggles with the Algebra in both of my Calculus classes( Intro Calc and Biz Calc w/ Analytical Geometry). There Algebra is no better then mine and most are obviously out of practice. So what do you have to say about that Skip? #2) I will have you and the others know this about me. I will take only so much mouth and verbal abuse(including subliminal text) I am taking 2 calc classes this Semester to get a better grip and plan to re take Trig next Semester as I found very challenging and like I already told Mark here on this forum... had a foriegn teacher who I personally felt was a horrible teacher/leader/instructor. I will however only asign so much blame on him and not if but when I retake will give 300% more this time around and make an A in Trig for personal triumpth. #3) As an aspiring math major, I plan to go far past the math that community colleges teach and will pound this forum all the way through. Do you hear me Skip? I heard you are quite the Genius yourself and very CLEVER and I mean no disrespect to you and/or Mark(whom I like a lot) but I will have you and the others know that when the going gets tough... I get 10x tougher. I was not top Mortgage Loan Officer for 7+ years at every and all co's I worked for nor the fund raising salesman who broke all the records the company had set ... (because I am weak!) Students need to be told firmly but assisted (I feel Mark is excellent in this area) ... and given onstructivle criticism not destrucively. Let me re emphacize the fact that I will pound pound pound this forum as I grow as a mathy and can always re created if I have too. Skip you might be thinking (bring it kid!) but I promise you that I will if I am not mentored but abused. Thanks Skip!

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