Can W|A solve partial differential equations?

Questions
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1

Hello,
I know the topic sounds very generic, but I’ve got a specific case that seems to be problematic. I don’t know if the issue lies in W|A not being able to solve the problem, or in me not understanding how to input the equations correctly.

I have a nonlinear PDE that I want to solve for ?.
When I type: “solve f(x)??(x)/?x+?(x)(?f(x)/?x+?G/?)=-((?M^2)/?)BV*e^(-x)” it doesn’t really give me any useful solution, but it seems to understand the syntax correctly.

I want to specify my f function and so I write:
“solve f(x)??(x)/?x+?(x)(?f(x)/?x+?G/?)=-((?M^2)/?)BVe^(-x) where f(x)=A1+(A2+A3)e^(-2x)"
or
"solve f(x)??(x)/?x+?(x)(?f(x)/?x+?G/?)=-((?M^2)/?)BV*e^(-x), f(x)=A1+(A2+A3)*e^(-2x)”
but now the site gives me no results at all, like it doesn’t understand what has been written.

I have a Pro account, I purchased it precisely to get help with equations like this. Do I need to rewrite the problem in some way or is it impossible to compute using ths web app?

2

WolframAlpha doesn’t appear to support user named functions. Uppercase variable names sometimes also cause problems. There is also a line length limit that sometimes requires a bit of skill in dividing a problem into parts or by solving problems one stage at a time. It does support a subset of Mathematica notation and at times this has let me solve problems that I couldn’t otherwise find a way to explain to WolframAlpha

DSolve[(a1+(a2+a3)E^(-2x))?'[x]+?[x](D[a1+(a2+a3)E^(-2x),x]+? g/?)== -(? m^2/?)b v*E^-x ,?,x]

or

WA link

returns a complicated exact solution. You might be able to see something in that or might be able to simplify that.

3

Thank you very much!

I’ve got to admit, I am disappointed in not receiving the option to look into the step-by-step process. In truth I was very much hoping for a hint on how to solve this specific equation, rather than a straightforward answer.

But still, thank you!

4

Hi Ewelina,

in the attached notebook I outline a step by step solution of your equation , but using lots of abbreviations.

Note the introduction of constants of integration c1, c2 and a0. These must be fixed by your initial-conditions.

I did NOT look at the resulting integrals, whether they could be solved and whether they yield the solutions given by DSolve (they should do), I leave this up to you.

wcomUntitled-3.nb (15.7 KB)

5

I really appreciate your help, I cannot thank you enough! I am grateful that you kindly took the time to walk me throught the problem, it’s very comprehensive. I didn’t ask for or expect this kind of help, so it’s a really nice surprise. Have a good day :slight_smile:

6

In the same way you can to find a solution to your 1st, more general equation (with appropriate abbreviations):

r = (a0 + 
Integrate[ u[t]/f[t]  Exp[Integrate[(A + D[f[tt], tt])/f[tt], {tt, c2, t}]], {t, c1, x}])
Exp[-Integrate[(D[f[tt], tt] + A)/f[tt], {tt, c2, x}]]

In[57]:= f[x] D[r, x] + r (D[f[x], x] + A) // FullSimplify

Out[57]= u[x]