23.2.54 problem 55

Internal problem ID [5409]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 55
Date solved : Tuesday, September 30, 2025 at 12:39:58 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

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

\begin{align*} y &= \frac {2}{3} x^{3}-x^{2}+c_1 \\ y &= c_1 \\ \end{align*}

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to c_1\\ y(x)&\to \frac {2 x^3}{3}-x^2+c_1 \end{align*}

✓ Sympy. Time used: 0.098 (sec). Leaf size: 17

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

\[ \left [ y{\left (x \right )} = C_{1} + \frac {2 x^{3}}{3} - x^{2}, \ y{\left (x \right )} = C_{1}\right ] \]