15.21.1 problem 23

Internal problem ID [3325]
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 : 23
Date solved : Tuesday, March 04, 2025 at 04:36:05 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 17

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

\begin{align*} y \left (x \right ) &= -\frac {x^{2}}{4} \\ y \left (x \right ) &= c_{1} \left (x +c_{1} \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 23

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

\begin{align*} y(x)\to c_1 (x+c_1) \\ y(x)\to -\frac {x^2}{4} \\ \end{align*}

✓ Sympy. Time used: 1.446 (sec). Leaf size: 10

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

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