35.2.11 problem 11

Internal problem ID [6103]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 2. Separable equations. page 398
Problem number : 11
Date solved : Wednesday, March 05, 2025 at 12:12:44 AM
CAS classification : [_quadrature]

\begin{align*} 2 y^{\prime }&=3 \left (y-2\right )^{{1}/{3}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Maple. Time used: 0.020 (sec). Leaf size: 9

ode:=2*diff(y(x),x) = 3*(y(x)-2)^(1/3); 
ic:=y(1) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 2+x^{{3}/{2}} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 12

ode=2*D[y[x],x]==3*(y[x]-2)^(1/3); 
ic={y[1]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^{3/2}+2 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*(y(x) - 2)**(1/3) + 2*Derivative(y(x), x),0) 
ics = {y(1): 3} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants