50.2.16 problem 2(e)

Internal problem ID [7822]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.3 SEPARABLE EQUATIONS. Page 12
Problem number : 2(e)
Date solved : Monday, January 27, 2025 at 03:24:15 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (-1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 20

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

\[ y = -1-\frac {\sqrt {-6 x^{3}+18 x +21}}{3} \]

✓ Solution by Mathematica

Time used: 0.156 (sec). Leaf size: 28

DSolve[{D[y[x],x]*(1+y[x])==1-x^2,{y[-1]==-2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {\sqrt {-2 x^3+6 x+7}}{\sqrt {3}}-1 \]