54.1.313 problem 319

Internal problem ID [11627]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 319
Date solved : Tuesday, September 30, 2025 at 09:49:09 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

\begin{align*} \left (7 x y^{3}+y-5 x \right ) y^{\prime }+y^{4}-5 y&=0 \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 34

ode:=(7*x*y(x)^3+y(x)-5*x)*diff(y(x),x)+y(x)^4-5*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ x +\frac {\frac {y^{5}}{5}-\frac {5 y^{2}}{2}-c_1}{\left (y^{3}-5\right )^{2} y} = 0 \]

✓ Mathematica. Time used: 0.129 (sec). Leaf size: 132

ode=-5*y[x] + y[x]^4 + (-5*x + y[x] + 7*x*y[x]^3)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [x=\exp \left (\int _1^{y(x)}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ) \int _1^{y(x)}\frac {\exp \left (-\int _1^{K[2]}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ) K[2]}{5 K[2]-K[2]^4}dK[2]+c_1 \exp \left (\int _1^{y(x)}\frac {7 K[1]^3-5}{5 K[1]-K[1]^4}dK[1]\right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((7*x*y(x)**3 - 5*x + y(x))*Derivative(y(x), x) + y(x)**4 - 5*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out