29.25.5 problem 702

Internal problem ID [5292]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 702
Date solved : Sunday, March 30, 2025 at 07:51:41 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (2-10 x^{2} y^{3}+3 y^{2}\right ) y^{\prime }&=x \left (1+5 y^{4}\right ) \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 27

ode:=(2-10*x^2*y(x)^3+3*y(x)^2)*diff(y(x),x) = x*(1+5*y(x)^4); 
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: 60.254 (sec). Leaf size: 2097

ode=(2-10*x^2*y[x]^3+3*y[x]^2)*D[y[x],x]==x*(1+5*y[x]^4); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 145.332 (sec). Leaf size: 4991

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*(5*y(x)**4 + 1) + (-10*x**2*y(x)**3 + 3*y(x)**2 + 2)*Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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