89.5.18 problem 18

Internal problem ID [24368]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 43
Problem number : 18
Date solved : Thursday, October 02, 2025 at 10:22:19 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 15

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

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

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 19

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

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

✓ Sympy. Time used: 1.023 (sec). Leaf size: 14

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)
 

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