60.2.377 problem 955

Internal problem ID [10951]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 955
Date solved : Sunday, March 30, 2025 at 07:29:53 PM
CAS classification : [_rational, [_Abel, `2nd type`, `class C`]]

\begin{align*} y^{\prime }&=\frac {-150 x^{3} y+60 x^{6}+350 x^{{7}/{2}}-150 x^{3}-125 y \sqrt {x}+250 x -125 \sqrt {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}}}{25 \left (-5 y+2 x^{3}+10 \sqrt {x}-5\right ) x} \end{align*}

✓ Maple. Time used: 0.026 (sec). Leaf size: 115

ode:=diff(y(x),x) = 1/25*(-150*x^3*y(x)+60*x^6+350*x^(7/2)-150*x^3-125*y(x)*x^(1/2)+250*x-125*x^(1/2)-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))/(-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}+2 \sqrt {x} \\ y &= \frac {\left (2 x^{3}+10 \sqrt {x}\right ) \sqrt {c_1 -2 \ln \left (x \right )}-2 x^{3}-10 \sqrt {x}+5}{5 \sqrt {c_1 -2 \ln \left (x \right )}-5} \\ y &= \frac {\left (2 x^{3}+10 \sqrt {x}\right ) \sqrt {c_1 -2 \ln \left (x \right )}+2 x^{3}+10 \sqrt {x}-5}{5 \sqrt {c_1 -2 \ln \left (x \right )}+5} \\ \end{align*}

✓ Mathematica. Time used: 0.668 (sec). Leaf size: 92

ode=D[y[x],x] == (-5*Sqrt[x] + 10*x + 40*x^(3/2) - 6*x^3 + 14*x^(7/2) + 24*x^4 + (12*x^6)/5 + (24*x^(13/2))/5 + (8*x^9)/25 - 5*Sqrt[x]*y[x] - 60*x*y[x] - 6*x^3*y[x] - 24*x^(7/2)*y[x] - (12*x^6*y[x])/5 + 30*Sqrt[x]*y[x]^2 + 6*x^3*y[x]^2 - 5*y[x]^3)/(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}-\frac {125}{125+\sqrt {-31250 \log (x)+c_1}} \\ y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\frac {125}{-125+\sqrt {-31250 \log (x)+c_1}} \\ y(x)\to \frac {2}{5} \left (x^3+5 \sqrt {x}\right ) \\ \end{align*}

✗ 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) + 350*x**(7/2) + 1000*x**(3/2) + 750*sqrt(x)*y(x)**2 - 125*sqrt(x)*y(x) - 125*sqrt(x) + 8*x**9 - 60*x**6*y(x) + 60*x**6 + 600*x**4 + 150*x**3*y(x)**2 - 150*x**3*y(x) - 150*x**3 - 1500*x*y(x) + 250*x - 125*y(x)**3)/(25*x*(10*sqrt(x) + 2*x**3 - 5*y(x) - 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out