60.1.302 problem 308

Internal problem ID [10316]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 308
Date solved : Sunday, March 30, 2025 at 04:01:25 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

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

\begin{align*} y &= 0 \\ y &= -\frac {\sqrt {-2 x^{2}+4 c_1}}{2} \\ y &= \frac {\sqrt {-2 x^{2}+4 c_1}}{2} \\ \end{align*}

✓ Mathematica. Time used: 0.077 (sec). Leaf size: 53

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

\begin{align*} y(x)\to 0 \\ y(x)\to -\sqrt {-\frac {x^2}{2}+2 c_1} \\ y(x)\to \sqrt {-\frac {x^2}{2}+2 c_1} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.574 (sec). Leaf size: 32

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

\[ \left [ y{\left (x \right )} = 0, \ y{\left (x \right )} = - \frac {\sqrt {C_{1} - 2 x^{2}}}{2}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} - 2 x^{2}}}{2}\right ] \]