89.30.11 problem 13

Internal problem ID [24928]
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 243
Problem number : 13
Date solved : Thursday, October 02, 2025 at 10:49:49 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

✓ Maple. Time used: 0.032 (sec). Leaf size: 42

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

\begin{align*} y &= k -2 \sqrt {a x} \\ y &= k +2 \sqrt {a x} \\ y &= \frac {c_1^{2} x +c_1 k +a}{c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 58

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

\begin{align*} y(x)&\to \frac {a}{c_1}+k+c_1 x\\ y(x)&\to \text {Indeterminate}\\ y(x)&\to k-2 \sqrt {a} \sqrt {x}\\ y(x)&\to 2 \sqrt {a} \sqrt {x}+k \end{align*}

✗ Sympy

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

Timed Out