85.1.11 problem 5 (d)

Internal problem ID [22416]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 1. Differential equations in general. A Exercises at page 12
Problem number : 5 (d)
Date solved : Thursday, October 02, 2025 at 08:38:41 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

ode:=diff(y(x),x)^3 = y(x); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 0 \]

✓ Mathematica. Time used: 0.204 (sec). Leaf size: 79

ode=D[y[x],{x,1}]^3==y[x]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 0\\ y(x)&\to \frac {2}{3} \sqrt {\frac {2}{3}} x^{3/2}\\ y(x)&\to \frac {2}{3} \sqrt {\frac {2}{3}} \left (-\sqrt [3]{-1} x\right )^{3/2}\\ y(x)&\to \frac {2}{3} \sqrt {\frac {2}{3}} \left ((-1)^{2/3} x\right )^{3/2} \end{align*}

✓ Sympy. Time used: 56.772 (sec). Leaf size: 153

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

\[ \left [ y{\left (x \right )} = \frac {\sqrt {- x - \sqrt {3} i x} \left (\sqrt {3} x + 3 i x\right )}{9}, \ y{\left (x \right )} = \frac {\sqrt {- x - \sqrt {3} i x} \left (- \sqrt {3} x - 3 i x\right )}{9}, \ y{\left (x \right )} = \frac {\sqrt {- x + \sqrt {3} i x} \left (\sqrt {3} x - 3 i x\right )}{9}, \ y{\left (x \right )} = \frac {\sqrt {- x + \sqrt {3} i x} \left (- \sqrt {3} x + 3 i x\right )}{9}, \ y{\left (x \right )} = - \frac {2 \sqrt {6} x^{\frac {3}{2}}}{9}, \ y{\left (x \right )} = \frac {2 \sqrt {6} x^{\frac {3}{2}}}{9}\right ] \]