29.10.20 problem 286

Internal problem ID [4886]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 286
Date solved : Sunday, March 30, 2025 at 04:08:59 AM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

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

\[ y = \frac {x^{2}}{3}+\frac {1}{3}+\frac {c_1}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.038 (sec). Leaf size: 27

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

\[ y(x)\to \frac {1}{3} \left (x^2+1\right )+\frac {c_1}{\sqrt {x^2+1}} \]

✓ Sympy. Time used: 0.471 (sec). Leaf size: 29

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

\[ y{\left (x \right )} = \frac {C_{1} \sqrt {x^{2} + 1} + x^{4} + 2 x^{2} + 1}{3 \left (x^{2} + 1\right )} \]