35.3.14 problem 14

Internal problem ID [6118]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 3. Linear First-Order Equations. page 403
Problem number : 14
Date solved : Sunday, March 30, 2025 at 10:39:12 AM
CAS classification : [_linear]

\begin{align*} x^{\prime }&=\frac {3 y^{{2}/{3}}-x}{3 y} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

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

\[ x = \frac {y +c_1}{y^{{1}/{3}}} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 15

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

\[ x(y)\to \frac {y+c_1}{\sqrt [3]{y}} \]

✓ Sympy. Time used: 0.190 (sec). Leaf size: 10

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

\[ x{\left (y \right )} = \frac {C_{1} + y}{\sqrt [3]{y}} \]