23.3.327 problem 329

Internal problem ID [6041]
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 : 329
Date solved : Tuesday, September 30, 2025 at 02:20:21 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

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

✓ Mathematica. Time used: 0.061 (sec). Leaf size: 41

ode=-((2 + 3*x)*y[x]) + (2 - x)*x*D[y[x],x] + x^2*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 e^x x-\frac {c_2 \left (e^x x^3 \operatorname {ExpIntegralEi}(-x)+x^2-x+2\right )}{6 x^2} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(2 - x)*Derivative(y(x), x) + (-3*x - 2)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False