23.2.22 problem 7

Internal problem ID [4139]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 3. Linear differential equations of second order. Exercises at page 31
Problem number : 7
Date solved : Sunday, March 30, 2025 at 02:40:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }-4 y&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

ode:=(x^2+1)*diff(diff(y(x),x),x)+x*diff(y(x),x)-4*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2 c_2 \,x^{2}+c_1 \sinh \left (2 \,\operatorname {arcsinh}\left (x \right )\right )+c_2 \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 25

ode=(1+x^2)*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to c_1 \cosh (2 \text {arcsinh}(x))+i c_2 \sinh (2 \text {arcsinh}(x)) \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x*Derivative(y(x), x) + (x**2 + 1)*Derivative(y(x), (x, 2)) - 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

False