23.3.426 problem 431

Internal problem ID [6140]
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 : 431
Date solved : Tuesday, September 30, 2025 at 02:22:14 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 2 \left (5+x \right ) y-x \left (7+2 x \right ) y^{\prime }+2 x^{2} y^{\prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 33

ode:=2*(5+x)*y(x)-x*(7+2*x)*diff(y(x),x)+2*x^2*diff(diff(y(x),x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (c_2 \sqrt {\pi }\, \operatorname {erf}\left (\sqrt {x}\right )-c_2 \sqrt {\pi }+c_1 \right ) x^{{5}/{2}}+c_2 \,x^{2} \]

✓ Mathematica. Time used: 0.1 (sec). Leaf size: 40

ode=2*(5 + x)*y[x] - x*(7 + 2*x)*D[y[x],x] + 2*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^{5/2}+2 c_2 x^2 \left (e^x \sqrt {x} \Gamma \left (\frac {1}{2},x\right )-1\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x**2*Derivative(y(x), (x, 2)) - x*(2*x + 7)*Derivative(y(x), x) + (2*x + 10)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False