78.8.23 problem 23

Internal problem ID [18150]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 23
Date solved : Monday, March 31, 2025 at 05:15:08 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

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

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

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 13

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

\[ y(x)\to c_1 \text {arcsinh}(x)+c_2 \]

✓ Sympy. Time used: 0.222 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = C_{1} + C_{2} \operatorname {asinh}{\left (x \right )} \]