54.1.29 problem 29

Internal problem ID [11343]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 29
Date solved : Tuesday, September 30, 2025 at 07:57:25 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

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

\[ y = \frac {3}{-1+3 \,{\mathrm e}^{-\frac {3 x^{2}}{2}} c_1} \]

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 46

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1] (K[1]+3)}dK[1]\&\right ]\left [\frac {x^2}{2}+c_1\right ]\\ y(x)&\to -3\\ y(x)&\to 0 \end{align*}

✓ Sympy. Time used: 11.743 (sec). Leaf size: 83

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

\[ \left [ y{\left (x \right )} = \frac {3 \left (\sqrt {e^{6 C_{1} + 3 x^{2}}} - e^{6 C_{1} + 3 x^{2}}\right )}{e^{6 C_{1} + 3 x^{2}} - 1}, \ y{\left (x \right )} = - \frac {3 \left (\sqrt {e^{6 C_{1} + 3 x^{2}}} + e^{6 C_{1} + 3 x^{2}}\right )}{e^{6 C_{1} + 3 x^{2}} - 1}\right ] \]