88.10.8 problem 8

Internal problem ID [24043]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 2. Differential equations of first order. Exercise at page 52
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:55:08 PM
CAS classification : [[_2nd_order, _missing_y], _Liouville, [_2nd_order, _reducible, _mu_xy]]

\begin{align*} x y^{\prime \prime }+{y^{\prime }}^{2} x -y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 13

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

\[ y = \ln \left (\frac {c_1 \,x^{2}}{2}+c_2 \right ) \]

✓ Mathematica. Time used: 0.18 (sec). Leaf size: 17

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

\begin{align*} y(x)&\to \log \left (x^2+2 c_1\right )+c_2 \end{align*}

✓ Sympy. Time used: 0.581 (sec). Leaf size: 10

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

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