29.4.1 problem 1

Internal problem ID [7254]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 1
Date solved : Tuesday, September 30, 2025 at 04:26:14 PM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 19

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

\[ -x +3-{\mathrm e}^{-\frac {x}{3}} c_1 +y^{{1}/{3}} = 0 \]

✓ Mathematica. Time used: 0.125 (sec). Leaf size: 39

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

\begin{align*} y(x)&\to \frac {1}{27} e^{-x} \left (\int _1^xe^{\frac {K[1]}{3}} K[1]dK[1]+3 c_1\right ){}^3 \end{align*}

✓ Sympy. Time used: 0.255 (sec). Leaf size: 78

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

\[ y{\left (x \right )} = C_{1}^{3} e^{- x} + 3 C_{1}^{2} x e^{- \frac {2 x}{3}} - 9 C_{1}^{2} e^{- \frac {2 x}{3}} + 3 C_{1} x^{2} e^{- \frac {x}{3}} - 18 C_{1} x e^{- \frac {x}{3}} + 27 C_{1} e^{- \frac {x}{3}} + x^{3} - 9 x^{2} + 27 x - 27 \]