23.2.103 problem 105

Internal problem ID [5458]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 105
Date solved : Tuesday, September 30, 2025 at 12:43:42 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

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

\begin{align*} y &= \frac {x^{2}}{2}+c_1 \\ y &= \ln \left (x \right )+c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 15

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

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