Internal problem ID [4944]
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]
\[ \boxed {y^{\prime }-\left (x -3\right ) \left (1+y\right )^{\frac {2}{3}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve(diff(y(x),x)=(x-3)*(y(x)+1)^(2/3),y(x), singsol=all)
\[ \frac {x^{2}}{2}-3 x -3 \left (y \left (x \right )+1\right )^{\frac {1}{3}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.197 (sec). Leaf size: 67
DSolve[y'[x]==(x-3)*(y[x]+1)^(2/3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{216} \left (x^6-18 x^5+6 (18+c_1) x^4-72 (3+c_1) x^3+12 c_1 (18+c_1) x^2-72 c_1{}^2 x+8 \left (-27+c_1{}^3\right )\right ) y(x)\to -1 \end{align*}