60.1.240 problem 245

Internal problem ID [10254]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 245
Date solved : Sunday, March 30, 2025 at 03:34:36 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: 0.686 (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: 0.372 (sec). Leaf size: 97

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]
 

\[ \text {Solve}\left [\int _1^{\frac {2^{2/3} \left (5 x^2 y(x)-23 x^4\right )}{\sqrt [3]{1495} \sqrt [3]{x^6} \left (2 x^2+y(x)\right )}}\frac {1}{K[1]^3-\frac {399 K[1]}{2990^{2/3}}+1}dK[1]+\frac {5\ 1495^{2/3} \left (x^6\right )^{2/3} \log (x)}{99 \sqrt [3]{2} x^4}=c_1,y(x)\right ] \]

✗ 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))) cannot be solved by the factorable group method