23.1.291 problem 283 (b)

Internal problem ID [4898]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 1. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF FIRST DEGREE, page 223
Problem number : 283 (b)
Date solved : Tuesday, September 30, 2025 at 08:55:58 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = \frac {a \,\operatorname {arcsinh}\left (x \right )+c_1}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 22

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

\begin{align*} y(x)&\to \frac {a \text {arcsinh}(x)+c_1}{\sqrt {x^2+1}} \end{align*}

✓ Sympy. Time used: 0.190 (sec). Leaf size: 17

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

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