60.2.261 problem 838

Internal problem ID [10835]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 838
Date solved : Sunday, March 30, 2025 at 07:11:23 PM
CAS classification : [_rational, _Riccati]

\begin{align*} y^{\prime }&=\frac {30 x^{3}+25 \sqrt {x}+25 y^{2}-20 x^{3} y-100 y \sqrt {x}+4 x^{6}+40 x^{{7}/{2}}+100 x}{25 x} \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 42

ode:=diff(y(x),x) = 1/25*(30*x^3+25*x^(1/2)+25*y(x)^2-20*x^3*y(x)-100*y(x)*x^(1/2)+4*x^6+40*x^(7/2)+100*x)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (10 c_1 -10 \ln \left (x \right )\right ) \sqrt {x}+2 c_1 \,x^{3}-2 x^{3} \ln \left (x \right )+5}{5 c_1 -5 \ln \left (x \right )} \]

✓ Mathematica. Time used: 0.304 (sec). Leaf size: 48

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

\begin{align*} y(x)\to \frac {2 x^3}{5}+2 \sqrt {x}+\frac {1}{-\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) - (40*x**(7/2) - 100*sqrt(x)*y(x) + 25*sqrt(x) + 4*x**6 - 20*x**3*y(x) + 30*x**3 + 100*x + 25*y(x)**2)/(25*x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (x**(3/2)*(40*x**(5/2) + 4*x**5 - 20*x**2*y(x) + 30*x**2 + 100)/25 + sqrt(x)*y(x)**2 + x*(1 - 4*y(x)))/x**(3/2) cannot be solved by the factorable group method