29.28.2 problem 799

Internal problem ID [5383]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 28
Problem number : 799
Date solved : Sunday, March 30, 2025 at 08:04:05 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _Clairaut]

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

✓ Maple. Time used: 0.031 (sec). Leaf size: 25

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

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 29

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

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

✓ Sympy. Time used: 2.318 (sec). Leaf size: 14

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

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