29.10.15 problem 281

Internal problem ID [4881]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 281
Date solved : Sunday, March 30, 2025 at 04:08:46 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\[ y = \sqrt {x^{2}+1}\, c_1 -x a \]

✓ Mathematica. Time used: 0.054 (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]
 

\[ y(x)\to -a x+c_1 \sqrt {x^2+1} \]

✓ Sympy. Time used: 1.663 (sec). Leaf size: 15

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)
 

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