54.2.103 problem 679

Internal problem ID [11977]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, Additional non-linear first order
Problem number : 679
Date solved : Tuesday, September 30, 2025 at 11:51:13 PM
CAS classification : [[_homogeneous, `class D`], _Riccati]

\begin{align*} y^{\prime }&=\frac {y+x^{3} \ln \left (x \right )+x^{4}+x^{3}+7 x y^{2} \ln \left (x \right )+7 x^{2} y^{2}+7 x y^{2}}{x} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 37

ode:=diff(y(x),x) = (y(x)+x^3*ln(x)+x^4+x^3+7*x*y(x)^2*ln(x)+7*x^2*y(x)^2+7*x*y(x)^2)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\tan \left (\frac {\left (6 x^{2} \ln \left (x \right )+4 x^{3}+3 x^{2}+12 c_1 \right ) \sqrt {7}}{12}\right ) x \sqrt {7}}{7} \]

✓ Mathematica. Time used: 0.088 (sec). Leaf size: 52

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

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

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x**4 + x**3*log(x) + x**3 + 7*x**2*y(x)**2 + 7*x*y(x)**2*log(x) + 7*x*y(x)**2 + y(x))/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE -x**3 - x**2*log(x) - x**2 - 7*x*y(x)**2 - 7*y(x)**2*log(x) - 7*y(x)**2 + Derivative(y(x), x) - y(x)/x cannot be solved by the factorable group method