89.32.8 problem 9

Internal problem ID [24968]
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. Miscellaneous Exercises at page 246
Problem number : 9
Date solved : Thursday, October 02, 2025 at 11:45:08 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} 4 x^{5} {y^{\prime }}^{2}+12 x^{4} y y^{\prime }+9&=0 \end{align*}

✓ Maple. Time used: 0.265 (sec). Leaf size: 53

ode:=4*x^5*diff(y(x),x)^2+12*x^4*y(x)*diff(y(x),x)+9 = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{x^{{3}/{2}}} \\ y &= -\frac {1}{x^{{3}/{2}}} \\ y &= \frac {c_1^{2} x^{3}+1}{2 c_1 \,x^{3}} \\ y &= \frac {x^{3}+c_1^{2}}{2 c_1 \,x^{3}} \\ \end{align*}

✓ Mathematica. Time used: 3.506 (sec). Leaf size: 75

ode=4*x^5*D[y[x],x]^2+12*x^4*y[x]*D[y[x],x]+9==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {1}{\sqrt {x^3 \text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}}\\ y(x)&\to \frac {1}{\sqrt {x^3 \text {sech}^2\left (\frac {3}{2} (-\log (x)+c_1)\right )}}\\ y(x)&\to -\frac {1}{x^{3/2}}\\ y(x)&\to \frac {1}{x^{3/2}} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x**5*Derivative(y(x), x)**2 + 12*x**4*y(x)*Derivative(y(x), x) + 9,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out