Internal problem ID [4436]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson
2018.
Section: Chapter 2, First order differential equations. Section 2.2, Separable Equations. Exercises. page
46
Problem number: 30.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\left (x -3\right ) \left (1+y\right )^{\frac {2}{3}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x)=(x-3)*(y(x)+1)^(2/3),y(x), singsol=all)
\[ \frac {x^{2}}{2}-3 x -3 \left (y \relax (x )+1\right )^{\frac {1}{3}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.315 (sec). Leaf size: 28
DSolve[y'[x]==(x-3)*(y[x]+1)^(2/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1+\frac {1}{216} ((x-6) x+2 c_1){}^3 \\ y(x)\to -1 \\ \end{align*}