Re: Bug in Homogeneous Solution of Differential equation?

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• Subject: [mg132385] Re: Bug in Homogeneous Solution of Differential equation?
• From: Murray Eisenberg <murray at math.umass.edu>
• Date: Sun, 2 Mar 2014 21:28:14 -0500 (EST)
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```I cannot understand what you mean by saying "select to solve as a
homogeneous equation", given that this is a non-linear differential
equation.

The correct Mathematica syntax is:

DSolve[{y'[t] == y[t]/(y[t] - t), y[0] == 1}, y[t], t]

This provides solution

{{y[t] -> t + Sqrt[1 + t^2]}}

along with warning that Inverse functions are being used, so some solutions may not be found.
On Mar 2, 2014, at 1:06 AM, amzoti <amzoti at gmail.com> wrote:

> I am using Mathematica V9.
>
> When I solve "= dy/dt = ( y )/ (y - t) , y(0) = 1" (using the WA approach within Mathematica), I get the correct answer.
>
> When I select "Solve as an exact equation" I also get the correct result.
>
> However, when I select to solve as a homogeneous equation, it leave the constant and does not appear ro converge.
>
> Is this a bug in step-by-step?
>
> Thanks -A
>

Murray Eisenberg                                murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 240 246-7240 (H)
University of Massachusetts
710 North Pleasant Street
Amherst, MA 01003-9305

```

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