47.3.26 problem 29

Internal problem ID [9774]
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 : 29
Date solved : Tuesday, September 30, 2025 at 06:41:02 PM
CAS classification : [[_homogeneous, `class G`], _rational]

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

✓ Maple. Time used: 1.634 (sec). Leaf size: 141

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

\begin{align*} y &= \frac {\operatorname {RootOf}\left (-4 \ln \left (x \right )+4 c_1 +3 \ln \left (-2+\textit {\_Z} \right )+\ln \left (\textit {\_Z} \right )-\ln \left (1+\sqrt {4 \textit {\_Z} +1}\right )+3 \ln \left (\sqrt {4 \textit {\_Z} +1}+3\right )+\ln \left (-1+\sqrt {4 \textit {\_Z} +1}\right )-3 \ln \left (\sqrt {4 \textit {\_Z} +1}-3\right )\right )}{x} \\ y &= \frac {\operatorname {RootOf}\left (-4 \ln \left (x \right )+4 c_1 +3 \ln \left (-2+\textit {\_Z} \right )+\ln \left (\textit {\_Z} \right )+\ln \left (1+\sqrt {4 \textit {\_Z} +1}\right )-3 \ln \left (\sqrt {4 \textit {\_Z} +1}+3\right )-\ln \left (-1+\sqrt {4 \textit {\_Z} +1}\right )+3 \ln \left (\sqrt {4 \textit {\_Z} +1}-3\right )\right )}{x} \\ \end{align*}

✓ Mathematica. Time used: 60.223 (sec). Leaf size: 4335

ode=y[x]==x*D[y[x],x]+x^3*(D[y[x],x])^2; 
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(-x**3*Derivative(y(x), x)**2 - x*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out