Internal problem ID [4267]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime }+y-x y^{\frac {2}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(x),x)+y(x)=x*y(x)^(2/3),y(x), singsol=all)
\[ -x +3-{\mathrm e}^{-\frac {x}{3}} c_{1}+y \relax (x )^{\frac {1}{3}} = 0 \]
✓ Solution by Mathematica
Time used: 0.284 (sec). Leaf size: 27
DSolve[y'[x]+y[x]==x*y[x]^(2/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-x} \left (e^{x/3} (x-3)+c_1\right ){}^3 \\ \end{align*}