89.7.6 problem 6

Internal problem ID [24437]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 61
Problem number : 6
Date solved : Thursday, October 02, 2025 at 10:31:54 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y x +\left (x^{2}-3 y\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.123 (sec). Leaf size: 985

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Mathematica. Time used: 60.023 (sec). Leaf size: 433

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

\begin{align*} y(x)&\to \frac {x^2}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,1\right ]}\\ y(x)&\to \frac {x^2}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,2\right ]}\\ y(x)&\to \frac {x^2}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,3\right ]}\\ y(x)&\to \frac {x^2}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,4\right ]}\\ y(x)&\to \frac {x^2}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,5\right ]}\\ y(x)&\to \frac {x^2}{3}-\frac {1}{3 \text {Root}\left [\text {$\#$1}^6 \left (x^{12}+e^{12 c_1}\right )-6 \text {$\#$1}^4 x^8+4 \text {$\#$1}^3 x^6+9 \text {$\#$1}^2 x^4-12 \text {$\#$1} x^2+4\&,6\right ]} \end{align*}

✗ Sympy

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

Timed Out