54.1.240 problem 245

Internal problem ID [11554]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 245
Date solved : Tuesday, September 30, 2025 at 09:00:39 PM
CAS classification : [[_homogeneous, `class G`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (2 x y+4 x^{3}\right ) y^{\prime }+y^{2}+112 x^{2} y&=0 \end{align*}

✓ Maple. Time used: 0.558 (sec). Leaf size: 31

ode:=(2*x*y(x)+4*x^3)*diff(y(x),x)+y(x)^2+112*x^2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {c_1}{x^{28} \operatorname {RootOf}\left (\textit {\_Z}^{360} x^{30}-24 \textit {\_Z}^{330} x^{30}-c_1 \right )^{330}} \]

✓ Mathematica. Time used: 22.868 (sec). Leaf size: 1453

ode=(2*x*y[x]+4*x^3)*D[y[x],x]+y[x]^2+112*x^2*y[x]==0; 
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(112*x**2*y(x) + (4*x**3 + 2*x*y(x))*Derivative(y(x), x) + y(x)**2,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (-112*x**2 - y(x))*y(x)/(2*x*(2*x**2 + y(x