40.5.7 problem 23

Internal problem ID [6672]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page 65
Problem number : 23
Date solved : Sunday, March 30, 2025 at 11:15:51 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

\begin{align*} {y^{\prime }}^{2}-x y^{\prime }+y&=0 \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 19

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

\begin{align*} y &= \frac {x^{2}}{4} \\ y &= c_1 \left (-c_1 +x \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 25

ode=D[y[x],x]^2-x*D[y[x],x]+y[x]==0; 
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: 2.061 (sec). Leaf size: 14

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)
 

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