Kernel crash solving ODE (Murphy #50), version 11.0.1 on windows

Question

This ODE (#50 from Murphy's ODE collection book) causes kernel crash each time

Here is the code

ClearAll[y, x]
DSolve[ y'[x] == Cos[2 x] + (Sin[2 x] + y[x]) y[x], y[x], x]

Screen shot below. Should this be tagged a bug? Does this happen on other platforms? I am using windows 7. I tried it on 10.4, and it also crashes there.

But on version 9.0, it does not crash, but it can't solve it:

Maple can solve it, but solution is complicated using HeunC special functions which Mathematica do not have

But Book also gives one simple solution y(x)=tan(x), which is easily verified to be true by Mathematica. (the other solution it gives is little more complicated).

eq = Hold [D[y[x], x] == Cos[2 x] + (Sin[2 x] + y[x]) y[x]];
Simplify[ReleaseHold[eq /. y[x] -> Tan[x]]]

Why does Mathematica kernel crash on this ODE?

Update:

Send bug report to Wolfram support, CASE:3806616 .

fyi, the book contains 2315 ODE's, which will take me long time to type and run. The current test report if you are interested is here. But it currently contains small number of ODE's from the book, will add more with time.

Answer 1

A bit too long for a comment. I think the hang is happening within Integrate:

Block[{Integrate},
  DSolve[y'[x] == Cos[2 x] + (Sin[2 x] + y[x]) y[x], y[x], x] /. {
    Integrate -> Inactive[Integrate]}
]

Edit

Here's the solution using withTimedIntegrate (as Micheal E2 pointed out in the comments):

withTimedIntegrate[DSolve[y'[x] == Cos[2 x] + (Sin[2 x] + y[x]) y[x], y[x], x], 1]

---

And just for fun, here's a way to solve this ODE:

• Substitute y[x] == v'[x]/v[x] to get

  v''[x] - Sin[2x]v'[x] + Cos[2x]v[x] == 0

• Next substitute Cos[x] == t to get

  (t^2 - 1)v''[t] + (2t^3 - t)v'[t] + (1 - 2t^2)v[t] == 0

• Then substitute v[t] == t w[t] to get

  t(t^2 - 1)w''[t] + (2t^4 + t^2 - 2)w'[t] == 0

• Substitute f[t] = w'[t] to get the first order separable equation

  t(t^2 - 1)f'[t] + (2t^4 + t^2 - 2)f[t] == 0

• This equation is easily solved, and the solution is

  {{f[t] -> (E^-t^2 C[1])/(t^2 Sqrt[1 - t^2])}}

• One can then perform all the back substitutions to get the final answer, which is where some nasty integrals will come into play.