54.3.254 problem 1270

Internal problem ID [12549]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1270
Date solved : Wednesday, October 01, 2025 at 02:06:33 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x^{2}+6 x +4\right ) y^{\prime \prime }+\left (10 x^{2}+21 x +8\right ) y^{\prime }+\left (12 x^{2}+17 x +8\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.067 (sec). Leaf size: 46

ode:=(2*x^2+6*x+4)*diff(diff(y(x),x),x)+(10*x^2+21*x+8)*diff(y(x),x)+(12*x^2+17*x+8)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (x +2\right )^{4} \left (c_2 \left (x +1\right )^{{5}/{2}} \operatorname {HeunC}\left (-1, \frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -x -1\right )+c_1 \operatorname {HeunC}\left (-1, -\frac {5}{2}, 4, -\frac {7}{4}, \frac {7}{2}, -x -1\right )\right ) \]

✓ Mathematica. Time used: 0.202 (sec). Leaf size: 120

ode=(8 + 17*x + 12*x^2)*y[x] + (8 + 21*x + 10*x^2)*D[y[x],x] + (4 + 6*x + 2*x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \exp \left (\int _1^x\frac {K[1]-2 K[1]^2}{4 K[1]^2+12 K[1]+8}dK[1]-\frac {1}{2} \int _1^x\left (-\frac {3}{K[2]+2}+5-\frac {3}{2 (K[2]+1)}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}\frac {K[1]-2 K[1]^2}{4 K[1]^2+12 K[1]+8}dK[1]\right )dK[3]+c_1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((2*x**2 + 6*x + 4)*Derivative(y(x), (x, 2)) + (10*x**2 + 21*x + 8)*Derivative(y(x), x) + (12*x**2 + 17*x + 8)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False