69.1.3 problem 4

Internal problem ID [17953]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 1. Basic concepts and definitions. Exercises page 18
Problem number : 4
Date solved : Thursday, October 02, 2025 at 02:31:06 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=y+3 y^{{1}/{3}} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 16

ode:=diff(y(x),x) = y(x)+3*y(x)^(1/3); 
dsolve(ode,y(x), singsol=all);
 

\[ 3-{\mathrm e}^{\frac {2 x}{3}} c_1 +y^{{2}/{3}} = 0 \]

✓ Mathematica. Time used: 1.253 (sec). Leaf size: 39

ode=D[y[x],x]==y[x]+3*y[x]^(1/3); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \left (-3+e^{\frac {2 (x+c_1)}{3}}\right ){}^{3/2}\\ y(x)&\to 0\\ y(x)&\to -3 i \sqrt {3} \end{align*}

✓ Sympy. Time used: 0.303 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*y(x)**(1/3) - y(x) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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