Wrong answer

[Tony K B]

got wrong answer for this ODE y''+y'+0.25y=0, Out put attached. Correct answer is (c_1+c_2*x)e^{-0.5x}. thank you

[Oscar Benjamin]

Thanks. This is a bug so best to open a GitHub issue:

https://github.com/sympy/sympy/issues

If you use rational numbers rather than floats it gives the correct answer:

In [9]: print(dsolve(nsimplify(ode), y))
Eq(y(x), (C1 + C2*x)*exp(-x/2))

In [10]: print(dsolve(ode, y))
Eq(y(x), (C1*sin(5.98941528027496e-13*x) +
C2*sin(6.42110952905754e-13*x) + C3*cos(5.98941528027496e-13*x) +
C4*cos(6.42110952905754e-13*x))*exp(-0.5*x))

There are two different bugs here. The first is roots being inaccurate
for floats:

In [6]: roots(x**2 + x + 0.25)
Out[6]: {-0.5 - 5.98941528027496e-13⋅ⅈ: 1, -0.5 + 6.42110952905754e-13⋅ⅈ: 1}

In [7]: roots(x**2 + x + Rational(0.25))
Out[7]: {-1/2: 2}

In general it is difficult to handle multiple roots in floating point.
I think it would be reasonable for roots to convert the floats to
rational and compute a square-free factorisation before doing anything
else though.

Somehow getting the wrong roots then results in having four rather
than two terms in the solution. There is a bug in the
nth_linear_constant_coefficient solver handling the roots somewhere.

--
Oscar

On Sun, 21 Jul 2024 at 10:33, Tony K B <tonn...@cet.ac.in> wrote:
>
> got wrong answer for this ODE y''+y'+0.25y=0, Out put attached. Correct answer is (c_1+c_2*x)e^{-0.5x}. thank you
>

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