60.2.376 problem 954

Internal problem ID [10950]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 954
Date solved : Sunday, March 30, 2025 at 07:29:47 PM
CAS classification : [_rational, _Abel]

\begin{align*} y^{\prime }&=\frac {150 x^{3}+125 \sqrt {x}+125+125 y^{2}-100 x^{3} y-500 y \sqrt {x}+20 x^{6}+200 x^{{7}/{2}}+500 x +125 y^{3}-150 x^{3} y^{2}-750 y^{2} \sqrt {x}+60 y x^{6}+600 y x^{{7}/{2}}+1500 x y-8 x^{9}-120 x^{{13}/{2}}-600 x^{4}-1000 x^{{3}/{2}}}{125 x} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 53

ode:=diff(y(x),x) = 1/125*(150*x^3+125*x^(1/2)+125+125*y(x)^2-100*x^3*y(x)-500*y(x)*x^(1/2)+20*x^6+200*x^(7/2)+500*x+125*y(x)^3-150*x^3*y(x)^2-750*y(x)^2*x^(1/2)+60*y(x)*x^6+600*y(x)*x^(7/2)+1500*x*y(x)-8*x^9-120*x^(13/2)-600*x^4-1000*x^(3/2))/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {18 x^{{7}/{2}}+145 \operatorname {RootOf}\left (-81 \int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} +\ln \left (x \right )+3 c_1 \right ) \sqrt {x}-15 \sqrt {x}+90 x}{45 \sqrt {x}} \]

✓ Mathematica. Time used: 0.311 (sec). Leaf size: 93

ode=D[y[x],x] == (1 + Sqrt[x] + 4*x - 8*x^(3/2) + (6*x^3)/5 + (8*x^(7/2))/5 - (24*x^4)/5 + (4*x^6)/25 - (24*x^(13/2))/25 - (8*x^9)/125 - 4*Sqrt[x]*y[x] + 12*x*y[x] - (4*x^3*y[x])/5 + (24*x^(7/2)*y[x])/5 + (12*x^6*y[x])/25 + y[x]^2 - 6*Sqrt[x]*y[x]^2 - (6*x^3*y[x]^2)/5 + y[x]^3)/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {\frac {-6 x^3-30 \sqrt {x}+5}{5 x}+\frac {3 y(x)}{x}}{\sqrt [3]{29} \sqrt [3]{\frac {1}{x^3}}}}\frac {1}{K[1]^3-\frac {3 K[1]}{29^{2/3}}+1}dK[1]=\frac {1}{9} 29^{2/3} \left (\frac {1}{x^3}\right )^{2/3} x^2 \log (x)+c_1,y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (-120*x**(13/2) + 600*x**(7/2)*y(x) + 200*x**(7/2) - 1000*x**(3/2) - 750*sqrt(x)*y(x)**2 - 500*sqrt(x)*y(x) + 125*sqrt(x) - 8*x**9 + 60*x**6*y(x) + 20*x**6 - 600*x**4 - 150*x**3*y(x)**2 - 100*x**3*y(x) + 150*x**3 + 1500*x*y(x) + 500*x + 125*y(x)**3 + 125*y(x)**2 + 125)/(125*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out