89.28.19 problem 19

Internal problem ID [24907]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 229
Problem number : 19
Date solved : Thursday, October 02, 2025 at 10:49:24 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.037 (sec). Leaf size: 20

ode:=x*y(x)*diff(y(x),x)^2+(x+y(x))*diff(y(x),x)+1 = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\begin{align*} y &= -\ln \left (x \right )+1 \\ y &= \sqrt {-2 x +3} \\ \end{align*}

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 24

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

\begin{align*} y(x)&\to \sqrt {3-2 x}\\ y(x)&\to 1-\log (x) \end{align*}

✗ Sympy

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

Timed Out