35.4.1 problem 1

Internal problem ID [6119]
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 : Monday, January 27, 2025 at 01:36:29 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.177 (sec). Leaf size: 27

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

\[ y(x)\to e^{-x} \left (e^{x/3} (x-3)+c_1\right ){}^3 \]