60.1.291 problem 297

Internal problem ID [10305]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 297
Date solved : Wednesday, March 05, 2025 at 10:09:50 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 2 x \left (y^{2}+5 x^{2}\right ) y^{\prime }+y^{3}-x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.624 (sec). Leaf size: 29

ode:=2*x*(y(x)^2+5*x^2)*diff(y(x),x)+y(x)^3-x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z}^{45} c_{1} x^{9}-\textit {\_Z}^{18}-6 \textit {\_Z}^{9}-9\right )^{{9}/{2}} x \]

✓ Mathematica. Time used: 0.122 (sec). Leaf size: 44

ode=2*x*(y[x]^2+5*x^2)*D[y[x],x]+y[x]^3-x^2*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]^2+5}{K[1] \left (K[1]^2+3\right )}dK[1]=-\frac {3 \log (x)}{2}+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.825 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2*y(x) + 2*x*(5*x**2 + y(x)**2)*Derivative(y(x), x) + y(x)**3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x \right )} = C_{1} + \log {\left (\frac {\left (3 + \frac {y^{2}{\left (x \right )}}{x^{2}}\right )^{\frac {2}{9}}}{\left (\frac {y{\left (x \right )}}{x}\right )^{\frac {10}{9}}} \right )} \]