89.32.11 problem 13

Internal problem ID [24971]
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. Miscellaneous Exercises at page 246
Problem number : 13
Date solved : Thursday, October 02, 2025 at 11:45:11 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _dAlembert]

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

✓ Maple. Time used: 0.034 (sec). Leaf size: 45

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

\begin{align*} y &= k +x -2 \sqrt {k x} \\ y &= k +x +2 \sqrt {k x} \\ y &= \frac {c_1 \left (c_1 x +k -x \right )}{c_1 -1} \\ \end{align*}

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 54

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

\begin{align*} y(x)&\to c_1 \left (x+\frac {k}{-1+c_1}\right )\\ y(x)&\to -2 \sqrt {k} \sqrt {x}+k+x\\ y(x)&\to \left (\sqrt {k}+\sqrt {x}\right )^2 \end{align*}

✗ Sympy

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

Timed Out