My Math Forum Finding the Particular Solution of diff eqn

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 November 18th, 2012, 04:06 PM #1 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Finding the Particular Solution of diff eqn dy/dx = 8x^3 -9x^2 + 4 and y =5, when x = 0 wanted to see this worked out in full ty
 November 18th, 2012, 04:10 PM #2 Senior Member   Joined: Nov 2011 Posts: 595 Thanks: 16 Re: Finding the Particular Solution of diff eqn Hi, Do you know what is the antiderivative of $x^3$, $x^2$, $x$...?
 November 18th, 2012, 04:25 PM #3 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: Finding the Particular Solution of diff eqn yes but am new to these x^3 = 3x^2 / 2
 November 18th, 2012, 05:05 PM #5 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: Finding the Particular Solution of diff eqn Thx Dougy
 November 18th, 2012, 05:17 PM #6 Senior Member   Joined: Nov 2011 Posts: 595 Thanks: 16 Re: Finding the Particular Solution of diff eqn Great! Sorry if I have been a bit harsh, I am glad you understood I am trying to go in a constructive way, not the opposite... it is very good that you are studying all these exercises at the end! Now think, could you solve another problem similar to this one? For instance could you do the equivalent problem $\frac{dy}{dx}=36x^5+5x^4-6x^2+8x$ and we want y to be equal to 5 at x=1, meaning y(1)=5? If you can do this, this means that you can do any problem like this with powers of x and when you see this in your exam that will be a peace of cake!
 November 18th, 2012, 06:35 PM #7 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: Finding the Particular Solution of diff eqn I think this is wrong. Maybe u can point out my errors 6x^6/6 + x^5/5 -2x^3/3 + 4x^2/2 + Csub1 ?
 November 18th, 2012, 07:02 PM #8 Senior Member   Joined: Nov 2011 Posts: 595 Thanks: 16 Re: Finding the Particular Solution of diff eqn Almost good! (but the fact that you still don't want to use latex ) You did a mistake in the coefficient in $\frac{x^5}{5}$ , it should be $x^5$ Do you see it? All the rest looks good! What about the value of the constant? y(1)=5, so what is Csub1? Plug x=1 and y(1)=5 and you will obtain an equation and you can solve for Csub1 and obtain its value. For the Latex thing, so you write things like y=5x^5+3x^2 for instance, now you write the exact same thing but inside the latex...you press the little box "latex" (I guess you can find it ) and write inside, not that complicate right? For each equation you have to start a new latex box and in between you write as you do normally. You want a sin, write \sin, a cos write \cos, an integral write \int, you want to write x/3 write \frac{x}{3} so like [ latex]\frac{x}{3}[/latex]= $\frac{x}{3}$ or [ latex]x^3[/latex]=$x^3$ edit: Actually I did not pay enough attention, all coefficients are wrong! I don't have time now to explain but you still have not understood this...try to work more on it and find your mistakes. Even if you have the correct solution to the other problem you will do wrong at your quiz on such questions as long as you don't know how to do them YOURSELF. We can discuss this later, try to work on it..you are not that far to understand!! Courage!
 November 18th, 2012, 07:26 PM #9 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: Finding the Particular Solution of diff eqn ok I will review in my book at work the problem again from start to finish. Also, I am going to post a new problem This one is an approximation problem. I will show as much work as I can ps...I will post it with LATEX or at least try
 November 18th, 2012, 08:07 PM #10 Senior Member   Joined: Aug 2012 From: South Carolina Posts: 866 Thanks: 0 Re: Finding the Particular Solution of diff eqn Here we go ..from start to finish... $\dy/dx$= $\8x^3 -9x^2 + 4$ find particular solution when y = 5, when x =0 $\int 8x^3-9x^2+4$dx y = $\8x^4/4 - 9x^3/3 +4x + c$ y = $2x^4 - 3x^3 + 4x + c$ now when y = 5 and x = 0 C must equal 5 ?

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