54.1.164 problem 167

Internal problem ID [11478]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 167
Date solved : Tuesday, September 30, 2025 at 08:31:26 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} 3 x^{2} y^{\prime }-7 y^{2}-3 x y-x^{2}&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 20

ode:=3*x^2*diff(y(x),x)-7*y(x)^2-3*x*y(x)-x^2 = 0; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.224 (sec). Leaf size: 29

ode=3*x^2*D[y[x],x] - 7*y[x]^2 - 3*x*y[x] - x^2==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x \tan \left (\frac {1}{3} \sqrt {7} (\log (x)+3 c_1)\right )}{\sqrt {7}} \end{align*}

✓ Sympy. Time used: 0.258 (sec). Leaf size: 49

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

\[ y{\left (x \right )} = \frac {\sqrt {7} x \left (i C_{1} + i e^{\frac {2 \sqrt {7} i \log {\left (x \right )}}{3}}\right )}{7 \left (C_{1} - e^{\frac {2 \sqrt {7} i \log {\left (x \right )}}{3}}\right )} \]