29.10.14 problem 280

Internal problem ID [4880]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 280
Date solved : Sunday, March 30, 2025 at 04:08:44 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: 19

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: 0.034 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.311 (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)
 

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