89.30.25 problem 27

Internal problem ID [24942]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 16. Equations of order one and higher degree. Exercises at page 243
Problem number : 27
Date solved : Thursday, October 02, 2025 at 11:36:22 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 5 {y^{\prime }}^{2}+3 x y^{\prime }-y&=0 \end{align*}

✓ Maple. Time used: 0.013 (sec). Leaf size: 85

ode:=5*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 (-30 x -10 \sqrt {9 x^{2}+20 y}\right )^{{3}/{2}}}+\frac {2 x}{5}-\frac {\sqrt {9 x^{2}+20 y}}{5} &= 0 \\ \frac {c_1}{\left (-30 x +10 \sqrt {9 x^{2}+20 y}\right )^{{3}/{2}}}+\frac {2 x}{5}+\frac {\sqrt {9 x^{2}+20 y}}{5} &= 0 \\ \end{align*}

✓ Mathematica. Time used: 17.598 (sec). Leaf size: 771

ode=5*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) + 5*Derivative(y(x), x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE 3*x/10 - sqrt(9*x**2 + 20*y(x))/10 + Derivative(y(x), x) cannot