60.1.316 problem 322

Internal problem ID [10330]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 322
Date solved : Sunday, March 30, 2025 at 04:10:36 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (10 x^{2} y^{3}-3 y^{2}-2\right ) y^{\prime }+5 x y^{4}+x&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

ode:=(10*x^2*y(x)^3-3*y(x)^2-2)*diff(y(x),x)+5*x*y(x)^4+x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \frac {5 y^{4} x^{2}}{2}+\frac {x^{2}}{2}-y^{3}-2 y+c_1 = 0 \]

✓ Mathematica. Time used: 60.252 (sec). Leaf size: 2097

ode=x + 5*x*y[x]^4 + (-2 - 3*y[x]^2 + 10*x^2*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 142.882 (sec). Leaf size: 4991

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*x*y(x)**4 + x + (10*x**2*y(x)**3 - 3*y(x)**2 - 2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \text {Solution too large to show} \]