76.44.1 problem Ex. 1

Internal problem ID [20250]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 99
Problem number : Ex. 1
Date solved : Thursday, October 02, 2025 at 05:37:49 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Maple. Time used: 0.020 (sec). Leaf size: 18

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

\[ y = -\frac {\ln \left (-a \left (c_1 x +c_2 \right )\right )}{a} \]

✓ Mathematica. Time used: 0.197 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to c_2-\frac {\log (a x+c_1)}{a} \end{align*}

✓ Sympy. Time used: 0.339 (sec). Leaf size: 12

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

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