15.21.3 problem 25

Internal problem ID [3327]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 39, page 179
Problem number : 25
Date solved : Sunday, March 30, 2025 at 01:37:02 AM
CAS classification : [[_homogeneous, `class G`], _Clairaut]

\begin{align*} y&=y^{\prime } x -\sqrt {y^{\prime }} \end{align*}

✓ Maple. Time used: 0.065 (sec). Leaf size: 21

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

\begin{align*} y &= -\frac {1}{4 x} \\ y &= c_1 x -\sqrt {c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 23

ode=y[x]==D[y[x],x]*x-Sqrt[D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to c_1 x-\sqrt {c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 4.534 (sec). Leaf size: 10

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

\[ y{\left (x \right )} = \frac {C_{1} \left (C_{1} x + 2\right )}{4} \]