36.1.33 problem 30

Internal problem ID [6288]
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
Date solved : Monday, January 27, 2025 at 01:54:45 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\left (x -3\right ) \left (y+1\right )^{{2}/{3}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 21

dsolve(diff(y(x),x)=(x-3)*(y(x)+1)^(2/3),y(x), singsol=all)
 

\[ \frac {x^{2}}{2}-3 x -3 \left (y+1\right )^{{1}/{3}}+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.206 (sec). Leaf size: 67

DSolve[D[y[x],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*}