29.10.16 problem 282

Internal problem ID [4882]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 282
Date solved : Sunday, March 30, 2025 at 04:08:50 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: 46

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

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

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.342 (sec). Leaf size: 26

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

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