Solving Differential equations using Mathematica

[moncholox]

Hi! I'm a mechanical engineering student from Argentina and this video is very helpful! thank you!

[yirafel1]

I graduated from UPR-Mayaguez with a BS in Chemical Engineer in 2008. Over this summer, I will start the PhD. program in Chemical Engineering and Material Science Department at the Michigan State University. I will use mathlab.... Thanks for the video!!!

[yynotx]

excellent overview offering rare clarity about differential classes and mathematica syntax. i really wish mathematica would fully support subscripted variables. thanks

[pmpalihena]

what do you need to press to get the answer, cuz after i insert the equation & press enter, it doesnt show me the answer.

[hifhif123]

@pmpalihena shift+enter, or the enter key on the number pad...

[lacsylle]

Oh that's very helpful for a beginner, thanks!

[topito2]

very informative, thank you!!!!

[Yereke]

Hello, I derived value of b by Taylor's series expansion, but now want to check my result with Mathematica 6.

Do you know how can I find b by Mathematica 6 from: pU(a+x-b)+(1-p)U(a-b)=U(a)? I used Solve[pU[a + x - b] + (1 - p) U[a - b] == U[a], b], but it soesn't give me an answer.

[14tobi07]

thanks man

[jkilha1]

Well done!

[hifhif123]

@jkilha1 Thanks. Check out others if you got the time. There is one other mathematica video, "how to plot a donut/ torus", it has no commentary though.

[chkg17]

I used:

DSolve[{y''[x] == 393.944 cos[x] + 57.734, y[0] == 0, y'[0] == 0}, y[x], x]

and the output was really long equation which is not a problem, but it had constants K's in it. What does that mean? Thanks for your help.

[hifhif123]

You made a small typo...

The "cos" should have an upper case C, i.e. Cos[x]

Solving in mathematica gives

{{y[x] -> 393.944+ 28.867 x^2 - 393.944 Cos[x] + (0.+ 0. i) Sin[x]}}

This one is quite straight forward to solve by hand, just integrate twice and apply the limits.

I don't know why it gives the unnecessary (0+0i) Sin[x]. This is probably due to the numerical nature of solvers.

[chkg17]

ah I got that thank you, but but what exactly does i mean? imaginary number? i.

If I want to solve for real I just ignore the i term right?

[hifhif123]

yes,i is the imaginary unit.

In this case you can ignore it since it's zero. Howevery if it was not zero then you couldn't ignore it.

The (0+0i)Sin[x] term is there probably due to the numerical methods used by programs to solve differential equations. You wouldn't put it in if you were to solve it manually.

[chkg17]

Thank you for all your help. We were able to solve our problem thanks to your help.

[gobitz]

very good dude... i hope i can master mathematica...

[hifhif123]

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