Math Is Fun Forum

Thanks so much Ricky for all of your help. Since you have nearly done half of the work, it is only fair that I post my result for parts c, d, and e. I have the whole thing in word document, but this was the graphs inserted in the assignment. I found C(t) = integral(K1+K2W(t))+c = 2t/5 + W/10 + 1.

Thanks for catching that mistake. Okay, so I have found a decent equation here, but need to know what method to use to integrate the pictured integral. My calc gives the pictured solution to that integral, but I don't know HOW to get there.

Also, I know this is skipping ahead, but my calculator can also solve the differential equation directly (handy tool for checking answers, but not a replacement for knowledge) and it gives me an implicit solution W^(1/4)= c*e^(-5t/6) +3 rather than solving for W directly. So can I just take the solution to the 4th power to solve for W directly? Since I have an initial condition W(0)=1, it would seem that I must find an explicit solution for W(t) to find C when I am done.

Finally, in part C of the assignment, it says "W(t) is as determined in part b." But W(t) is not found in equation (3), only dW/dt is. So it would seem that I would substitute

Now for part b I am given values for constants, but as you can see, the differential equation is much more complicated that in part a. How would I go about solving this equation for W(t)? Is it so simple that is still separable?

This conversion is QUITE inconvenient for differentiation/integration as the output is either not similar to the result found by standard methods (everything is written backwards ((100-t) vs (100-t)) and sometimes leads to failure to perform calculus functions on expressions. Can I prevent these conversions?

I am wondering why the calculator INSISTS on this representation.

Hi Jane, I thoroughly appreciate your help. Seeing how you broke things down to their definitions helps alot. But there seem to be tricks that you need along the way. I am still having a little trouble justifying step 3 in problem 1a though:  I am not exactly sure what property I can pin this on. Thank you so much. I am glad there is someone out there that has actually seen this stuff before!

Hi, I am new to the boards. I was wondering how people get their equation symbols into their posts, like Jane did above. You can also just cop and paste the symbols from the top of this page, correct?