23.3.280 problem 282

Internal problem ID [5994]
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 : 282
Date solved : Tuesday, September 30, 2025 at 02:07:30 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = \left (a +x \right ) c_1 +c_2 \,{\mathrm e}^{\frac {a}{x}} x \]

✓ Mathematica. Time used: 0.091 (sec). Leaf size: 26

ode=-y[x] + (a + 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 \frac {c_2 (a+x)}{a^2}+c_1 x e^{a/x} \end{align*}

✗ Sympy

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

NotImplementedError : The given ODE Derivative(y(x), x) - (-x**2*Derivative(y(x), (x, 2)) + y(x))/(a