75.3.25 problem 25

Internal problem ID [19929]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 25
Date solved : Thursday, October 02, 2025 at 05:02:33 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} \left (x^{2}+2 y x \right ) y^{\prime }-3 x^{2}+2 y x -y^{2}&=0 \end{align*}

✓ Maple. Time used: 0.022 (sec). Leaf size: 55

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

\[ -\ln \left (\frac {-3 x^{2}+3 x y+y^{2}}{x^{2}}\right )-\frac {4 \sqrt {21}\, \operatorname {arctanh}\left (\frac {\left (2 y+3 x \right ) \sqrt {21}}{21 x}\right )}{21}-\ln \left (x \right )-c_1 = 0 \]

✓ Mathematica. Time used: 0.101 (sec). Leaf size: 68

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

\[ \text {Solve}\left [\frac {1}{21} \left (21-2 \sqrt {21}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {21}-3\right )+\frac {1}{21} \left (21+2 \sqrt {21}\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {21}+3\right )=-\log (x)+c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out