23.3.250 problem 252

Internal problem ID [5964]
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 : 252
Date solved : Tuesday, September 30, 2025 at 02:07:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.009 (sec). Leaf size: 27

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

\[ y = \frac {\left (c_1 x +c_2 \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_2 x -c_1 \right )}{x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to x (c_1 j_1(x)-c_2 y_1(x)) \end{align*}

✓ Sympy. Time used: 0.039 (sec). Leaf size: 20

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

\[ y{\left (x \right )} = \sqrt {x} \left (C_{1} J_{\frac {3}{2}}\left (x\right ) + C_{2} Y_{\frac {3}{2}}\left (x\right )\right ) \]