29.27.30 problem 796

Internal problem ID [5380]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 27
Problem number : 796
Date solved : Sunday, March 30, 2025 at 08:04:00 AM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.034 (sec). Leaf size: 85

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

\begin{align*} \frac {c_1}{\left (-6 x -2 \sqrt {9 x^{2}+4 y}\right )^{{3}/{2}}}+\frac {2 x}{5}-\frac {\sqrt {9 x^{2}+4 y}}{5} &= 0 \\ \frac {c_1}{\left (-6 x +2 \sqrt {9 x^{2}+4 y}\right )^{{3}/{2}}}+\frac {2 x}{5}+\frac {\sqrt {9 x^{2}+4 y}}{5} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 13.92 (sec). Leaf size: 776

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

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), x) - y(x) + Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE 3*x/2 - sqrt(9*x**2 + 4*y(x))/2 + Derivative(y(x), x) cannot be solved by the factorable group method