60.1.44 problem 44

Internal problem ID [10058]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 44
Date solved : Wednesday, March 05, 2025 at 08:09:06 AM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 53

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

\begin{align*} y &= -\frac {2}{\sqrt {-4 a \,x^{2}+4 c_{1} {\mathrm e}^{2 x^{2}}-2 a}} \\ y &= \frac {2}{\sqrt {-4 a \,x^{2}+4 c_{1} {\mathrm e}^{2 x^{2}}-2 a}} \\ \end{align*}

✓ Mathematica. Time used: 7.488 (sec). Leaf size: 70

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

\begin{align*} y(x)\to -\frac {1}{\sqrt {-\frac {1}{2} a \left (2 x^2+1\right )+c_1 e^{2 x^2}}} \\ y(x)\to \frac {1}{\sqrt {-\frac {1}{2} a \left (2 x^2+1\right )+c_1 e^{2 x^2}}} \\ y(x)\to 0 \\ \end{align*}

✓ Sympy. Time used: 1.076 (sec). Leaf size: 63

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

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