54.3.248 problem 1264

Internal problem ID [12543]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1264
Date solved : Wednesday, October 01, 2025 at 01:57:50 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}+3 x +4\right ) y^{\prime \prime }+\left (x^{2}+x +1\right ) y^{\prime }-\left (2 x +3\right ) y&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 19

ode:=(x^2+3*x+4)*diff(diff(y(x),x),x)+(x^2+x+1)*diff(y(x),x)-(2*x+3)*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_1 \,{\mathrm e}^{-x}+c_2 \left (x^{2}+x +3\right ) \]

✓ Mathematica. Time used: 0.188 (sec). Leaf size: 121

ode=(-3 - 2*x)*y[x] + (1 + x + x^2)*D[y[x],x] + (4 + 3*x + 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] (K[1]+5)+7}{2 K[1] (K[1]+3)+8}dK[1]-\frac {1}{2} \int _1^x\frac {K[2]^2+K[2]+1}{K[2] (K[2]+3)+4}dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}-\frac {K[1]^2+5 K[1]+7}{2 K[1]^2+6 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 - 3)*y(x) + (x**2 + x + 1)*Derivative(y(x), x) + (x**2 + 3*x + 4)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False