60.2.294 problem 872

Internal problem ID [10868]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 872
Date solved : Sunday, March 30, 2025 at 07:17:45 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=\frac {-30 x^{3} y+12 x^{6}+70 x^{{7}/{2}}-30 x^{3}-25 y \sqrt {x}+50 x -25 \sqrt {x}-25}{5 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 49

ode:=diff(y(x),x) = 1/5*(-30*x^3*y(x)+12*x^6+70*x^(7/2)-30*x^3-25*y(x)*x^(1/2)+50*x-25*x^(1/2)-25)/(-5*y(x)+2*x^3+10*x^(1/2)-5)/x; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= \frac {2 x^{3}}{5}-\sqrt {c_1 +2 \ln \left (x \right )}+2 \sqrt {x}-1 \\ y &= \frac {2 x^{3}}{5}+\sqrt {c_1 +2 \ln \left (x \right )}+2 \sqrt {x}-1 \\ \end{align*}

✓ Mathematica. Time used: 0.47 (sec). Leaf size: 92

ode=D[y[x],x] == (-5 - 5*Sqrt[x] + 10*x - 6*x^3 + 14*x^(7/2) + (12*x^6)/5 - 5*Sqrt[x]*y[x] - 6*x^3*y[x])/(x*(-5 + 10*Sqrt[x] + 2*x^3 - 5*y[x])); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\sqrt {-\frac {1}{x}} \sqrt {-x (2 \log (x)+1+c_1)}-1 \\ y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\left (-\frac {1}{x}\right )^{3/2} x \sqrt {-x (2 \log (x)+1+c_1)}-1 \\ \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (70*x**(7/2) - 25*sqrt(x)*y(x) - 25*sqrt(x) + 12*x**6 - 30*x**3*y(x) - 30*x**3 + 50*x - 25)/(5*x*(10*sqrt(x) + 2*x**3 - 5*y(x) - 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out