# dsolve fails for a system of independent equations #15574

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opened this Issue Nov 30, 2018 · 3 comments

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### WFKala commented Nov 30, 2018

 Test case in Sympy 1.3: from sympy import * x = symbols('x') f1 = Function("f1")(x) f2 = Function("f2")(x) f3 = Function("f3")(x) sol = dsolve([ Eq(Derivative(f1,x), f1), Eq(Derivative(f2,x), f2), ] ) display(sol) sol = dsolve([ Eq(Derivative(f1,x), f1), Eq(Derivative(f2,x), f2), Eq(Derivative(f3,x), f3), ] ) display(sol) Result [Eq(f1(x), C1exp(x)), Eq(f2(x), C2exp(x))] [Eq(f1(x), C1*exp(x)), False, False] If there are two independent equations the result is correct. If there are three independent equations, the results from dsolve is wrong : it should be solvable but it is not in `dsolve`.
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### oscarbenjamin commented Nov 30, 2018

 Thanks for reporting this. This is still the case on master. In fact for 4 equations it's even worse: ```In [12]: f1, f2, f3, f4 = symbols('f1 f2 f3 f4', cls=Function) In [13]: eqs = [Eq(f(x).diff(x), f(x)) for f in (f1, f2, f3, f4)] In [14]: eqs Out[14]: ⎡d d d d ⎤ ⎢──(f₁(x)) = f₁(x), ──(f₂(x)) = f₂(x), ──(f₃(x)) = f₃(x), ──(f₄(x)) = f₄(x)⎥ ⎣dx dx dx dx ⎦ In [15]: dsolve(eqs[:2]) Out[15]: ⎡ x x⎤ ⎣f₁(x) = C₁⋅ℯ , f₂(x) = C₂⋅ℯ ⎦ In [16]: dsolve(eqs[:3]) Out[16]: ⎡ x ⎤ ⎣f₁(x) = C₁⋅ℯ , False, False⎦ In [17]: dsolve(eqs[:4]) Out[17]: ⎡ 2 x 3 x 2 x ⎤ ⎢ x x C₃⋅x ⋅ℯ C₄⋅x ⋅ℯ x x C₄⋅x ⋅ℯ x x x⎥ ⎢f₁(x) = C₁⋅ℯ + C₂⋅x⋅ℯ + ──────── + ────────, f₂(x) = C₂⋅ℯ + C₃⋅x⋅ℯ + ────────, f₃(x) = C₃⋅ℯ + C₄⋅x⋅ℯ , f₄(x) = C₄⋅ℯ ⎥ ⎣ 2 6 2 ⎦``` The case with 4 equations is fixed by #15449: ```In [4]: dsolve(eqs[:4]) Out[4]: ⎡ x x x x⎤ ⎣f₁(x) = C₁⋅ℯ , f₂(x) = C₂⋅ℯ , f₃(x) = C₃⋅ℯ , f₄(x) = C₄⋅ℯ ⎦``` The other cases would be fixed by removing the various 2eq and 3eq functions that handle them and leaving it the fixed neq solver provided by #15449.
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### oscarbenjamin commented Nov 30, 2018

 This is related to #15474
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### oscarbenjamin commented Nov 30, 2018

 Also #15407

### skirpichev added a commit to skirpichev/diofant that referenced this issue Dec 1, 2018

``` Add regression test ```
`Closes sympy/sympy#15574`
``` 9e09f6b ```