47.3.24 problem 27

Internal problem ID [9772]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 99. Clairaut equation. EXERCISES Page 320
Problem number : 27
Date solved : Tuesday, September 30, 2025 at 06:41:00 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: 0.033 (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: 18.729 (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 be solved by the factorable group method