23.4.124 problem 124

Internal problem ID [6426]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 124
Date solved : Tuesday, September 30, 2025 at 02:56:34 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y y^{\prime \prime }&=a \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 53

ode:=y(x)*diff(diff(y(x),x),x) = a; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} \int _{}^{y}\frac {1}{\sqrt {2 a \ln \left (\textit {\_a} \right )-c_1}}d \textit {\_a} -x -c_2 &= 0 \\ -\int _{}^{y}\frac {1}{\sqrt {2 a \ln \left (\textit {\_a} \right )-c_1}}d \textit {\_a} -x -c_2 &= 0 \\ \end{align*}

✓ Mathematica. Time used: 60.187 (sec). Leaf size: 111

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

\begin{align*} y(x)&\to \exp \left (-\frac {2 a \text {erf}^{-1}\left (-i \sqrt {\frac {2}{\pi }} \sqrt {a e^{\frac {c_1}{a}} (x+c_2){}^2}\right ){}^2+c_1}{2 a}\right )\\ y(x)&\to \exp \left (-\frac {2 a \text {erf}^{-1}\left (i \sqrt {\frac {2}{\pi }} \sqrt {a e^{\frac {c_1}{a}} (x+c_2){}^2}\right ){}^2+c_1}{2 a}\right ) \end{align*}

✗ Sympy

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

Timed Out