23.2.188 problem 193

Internal problem ID [5543]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 2. THE DIFFERENTIAL EQUATION IS OF FIRST ORDER AND OF SECOND OR HIGHER DEGREE, page 278
Problem number : 193
Date solved : Tuesday, September 30, 2025 at 12:51:49 PM
CAS classification : [[_homogeneous, `class G`]]

\begin{align*} x^{8} {y^{\prime }}^{2}+3 x y^{\prime }+9 y&=0 \end{align*}

✓ Maple. Time used: 0.160 (sec). Leaf size: 45

ode:=x^8*diff(y(x),x)^2+3*x*diff(y(x),x)+9*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {1}{4 x^{6}} \\ y &= \frac {-x^{3}+c_1}{x^{3} c_1^{2}} \\ y &= \frac {-x^{3}-c_1}{x^{3} c_1^{2}} \\ \end{align*}

✓ Mathematica. Time used: 0.339 (sec). Leaf size: 130

ode=x^8 (D[y[x],x])^2+3 x D[y[x],x]+9 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} \text {Solve}\left [\frac {x \sqrt {4 x^6 y(x)-1} \arctan \left (\sqrt {4 x^6 y(x)-1}\right )}{3 \sqrt {x^2-4 x^8 y(x)}}-\frac {1}{6} \log (y(x))=c_1,y(x)\right ]\\ \text {Solve}\left [\frac {\sqrt {x^2-4 x^8 y(x)} \arctan \left (\sqrt {4 x^6 y(x)-1}\right )}{3 x \sqrt {4 x^6 y(x)-1}}-\frac {1}{6} \log (y(x))=c_1,y(x)\right ]\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 2.983 (sec). Leaf size: 12

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**8*Derivative(y(x), x)**2 + 3*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} \left (- C_{1} + \frac {2}{x^{3}}\right )}{4} \]