60.1.165 problem 168
Internal
problem
ID
[10179]
Book
:
Differential
Gleichungen,
E.
Kamke,
3rd
ed.
Chelsea
Pub.
NY,
1948
Section
:
Chapter
1,
linear
first
order
Problem
number
:
168
Date
solved
:
Sunday, March 30, 2025 at 03:21:52 PM
CAS
classification
:
[_rational, _Riccati]
\begin{align*} 3 \left (x^{2}-4\right ) y^{\prime }+y^{2}-x y-3&=0 \end{align*}
✓ Maple. Time used: 0.019 (sec). Leaf size: 167
ode:=3*(x^2-4)*diff(y(x),x)+y(x)^2-x*y(x)-3 = 0;
dsolve(ode,y(x), singsol=all);
\[
y = -\frac {\left (x +2\right )^{2} \left (\left (-2 x -4\right )^{{1}/{3}} \left (x -2\right ) \operatorname {hypergeom}\left (\left [-\frac {1}{6}, \frac {1}{6}\right ], \left [-\frac {1}{3}\right ], -\frac {4}{x -2}\right )+24 \operatorname {hypergeom}\left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {7}{3}\right ], -\frac {4}{x -2}\right ) c_1 \right )}{\left (-2 x -4\right )^{{1}/{3}} \left (x -2\right ) \left (x +2\right )^{2} \operatorname {hypergeom}\left (\left [-\frac {1}{6}, \frac {1}{6}\right ], \left [-\frac {1}{3}\right ], -\frac {4}{x -2}\right )+32 \left (x +2\right )^{2} \left (x -\frac {5}{4}\right ) c_1 \operatorname {hypergeom}\left (\left [\frac {5}{6}, \frac {7}{6}\right ], \left [\frac {7}{3}\right ], -\frac {4}{x -2}\right )+4 \left (\frac {x +2}{x -2}\right )^{{1}/{6}} \left (\left (-2 x -4\right )^{{1}/{3}} \left (x +2\right ) \operatorname {HeunCPrime}\left (0, -\frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right )+24 \operatorname {HeunCPrime}\left (0, \frac {4}{3}, -\frac {1}{3}, 0, \frac {25}{36}, \frac {4}{x +2}\right ) c_1 \right ) \left (x -2\right )^{2}}
\]
✓ Mathematica. Time used: 0.415 (sec). Leaf size: 135
ode=3*(x^2-4)*D[y[x],x] + y[x]^2 - x*y[x] - 3==0;
ic={};
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
\begin{align*}
y(x)\to \frac {-2 c_1 x P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+3 c_1 P_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )-2 x Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+3 Q_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}{Q_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )+c_1 P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )} \\
y(x)\to \frac {3 P_{\frac {5}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}{P_{-\frac {1}{6}}^{\frac {1}{3}}\left (\frac {x}{2}\right )}-2 x \\
\end{align*}
✗ Sympy
from sympy import *
x = symbols("x")
y = Function("y")
ode = Eq(-x*y(x) + (3*x**2 - 12)*Derivative(y(x), x) + y(x)**2 - 3,0)
ics = {}
dsolve(ode,func=y(x),ics=ics)
TypeError : bad operand type for unary -: list