23.2.66 problem 68

Internal problem ID [5421]
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 : 68
Date solved : Tuesday, September 30, 2025 at 12:41:01 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}-2 \left (1-3 y\right ) y^{\prime }-\left (4-9 y\right ) y&=0 \end{align*}

✓ Maple. Time used: 1.155 (sec). Leaf size: 123

ode:=diff(y(x),x)^2-2*(1-3*y(x))*diff(y(x),x)-(4-9*y(x))*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {\operatorname {RootOf}\left (\textit {\_Z}^{8} {\mathrm e}^{24 x}+24 \textit {\_Z}^{7} {\mathrm e}^{24 x}+240 \textit {\_Z}^{6} {\mathrm e}^{24 x}+1280 \textit {\_Z}^{5} {\mathrm e}^{24 x}+\left (3840 \,{\mathrm e}^{24 x}-1458 c_1 \,{\mathrm e}^{12 x}\right ) \textit {\_Z}^{4}+\left (6144 \,{\mathrm e}^{24 x}+75816 c_1 \,{\mathrm e}^{12 x}\right ) \textit {\_Z}^{3}+\left (4096 \,{\mathrm e}^{24 x}-209952 c_1 \,{\mathrm e}^{12 x}\right ) \textit {\_Z}^{2}-23328 c_1 \textit {\_Z} \,{\mathrm e}^{12 x}+531441 c_1^{2}-11664 c_1 \,{\mathrm e}^{12 x}\right )}{9}+\frac {4}{9} \\ y &= {\frac {4}{9}} \\ \end{align*}

✓ Mathematica. Time used: 60.183 (sec). Leaf size: 4769

ode=(D[y[x],x])^2-2*(1-3*y[x])*D[y[x],x]-(4-9*y[x])*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Too large to display

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((6*y(x) - 2)*Derivative(y(x), x) + (9*y(x) - 4)*y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out