60.1.310 problem 316

Internal problem ID [10324]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 316
Date solved : Sunday, March 30, 2025 at 04:10:19 PM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.017 (sec). Leaf size: 60

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

\begin{align*} y &= 0 \\ y &= \sqrt {2}\, \sqrt {-\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \operatorname {Ei}_{1}\left (\textit {\_Z} \right )+4 \,{\mathrm e}^{\textit {\_Z}} c_1 -4 x \right )} \\ y &= -\sqrt {2}\, \sqrt {-\operatorname {RootOf}\left ({\mathrm e}^{\textit {\_Z}} \operatorname {Ei}_{1}\left (\textit {\_Z} \right )+4 \,{\mathrm e}^{\textit {\_Z}} c_1 -4 x \right )} \\ \end{align*}

✓ Mathematica. Time used: 0.317 (sec). Leaf size: 53

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

\begin{align*} y(x)\to 0 \\ \text {Solve}\left [x&=-\frac {1}{4} e^{-\frac {1}{2} y(x)^2} \operatorname {ExpIntegralEi}\left (\frac {y(x)^2}{2}\right )+c_1 e^{-\frac {1}{2} y(x)^2},y(x)\right ] \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 4.075 (sec). Leaf size: 3

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

\[ y{\left (x \right )} = 0 \]