23.3.506 problem 512

Internal problem ID [6220]
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 : 512
Date solved : Tuesday, September 30, 2025 at 02:36:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

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

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

\[ y = c_1 \sinh \left (x +\ln \left (x \right )\right )+c_2 \cosh \left (x +\ln \left (x \right )\right ) \]

✓ Mathematica. Time used: 2.025 (sec). Leaf size: 25

ode=-((1 + x)^3*y[x]) + x*D[y[x],x] + x^2*(1 + x)*D[y[x],{x,2}] == 0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 \cosh (x+\log (x))+i c_2 \sinh (x+\log (x)) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*(x + 1)*Derivative(y(x), (x, 2)) + x*Derivative(y(x), x) - (x + 1)**3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False