54.1.145 problem 148

Internal problem ID [11459]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 148
Date solved : Tuesday, September 30, 2025 at 08:26:49 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

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

\[ y = \frac {\operatorname {arcsinh}\left (x \right )+c_1}{\sqrt {x^{2}+1}} \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.194 (sec). Leaf size: 15

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

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