54.1.146 problem 149

Internal problem ID [11460]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 149
Date solved : Tuesday, September 30, 2025 at 08:26:50 PM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 27

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

\begin{align*} y(x)&\to \frac {1}{3} \left (x^2+1\right )+\frac {c_1}{\sqrt {x^2+1}} \end{align*}

✓ Sympy. Time used: 0.285 (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)
 

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