23.3.410 problem 415

Internal problem ID [6124]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 415
Date solved : Tuesday, September 30, 2025 at 02:21:57 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x \left (7+6 x \right ) y+\left (1-x \right ) x y^{\prime }+\left (-x^{2}-x +2\right ) y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.005 (sec). Leaf size: 43

ode:=x*(7+6*x)*y(x)+(1-x)*x*diff(y(x),x)+(-x^2-x+2)*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 195 c_2 \,{\mathrm e}^{-5+2 x} \left (x -1\right ) \operatorname {Ei}_{1}\left (5 x -5\right )-c_2 \left (x +44\right ) {\mathrm e}^{-3 x}+c_1 \,{\mathrm e}^{2 x} \left (x -1\right ) \]

✓ Mathematica. Time used: 0.432 (sec). Leaf size: 52

ode=x*(7 + 6*x)*y[x] + (1 - x)*x*D[y[x],x] + (2 - x - x^2)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 39 c_2 e^{2 x-5} (x-1) \operatorname {ExpIntegralEi}(5-5 x)+c_1 \left (-e^{2 x}\right ) (x-1)+\frac {1}{5} c_2 e^{-3 x} (x+44) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*(1 - x)*Derivative(y(x), x) + x*(6*x + 7)*y(x) + (-x**2 - x + 2)*Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False