36.3.3 problem 3

Internal problem ID [6324]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 3
Date solved : Monday, January 27, 2025 at 01:56:34 PM
CAS classification : [_separable]

\begin{align*} \sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 21

dsolve(sqrt(-2*y(x)-y(x)^2)+(3+2*x-x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -1+\sin \left (-\frac {\ln \left (x +1\right )}{4}+\frac {\ln \left (x -3\right )}{4}+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 2.516 (sec). Leaf size: 99

DSolve[Sqrt[-2*y[x]-y[x]^2]+(3+2*x-x^2)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 \cos \left (\frac {1}{4} (\log (3-x)-\log (x+1)+4 c_1)\right )-i \sqrt {3} \sin \left (\frac {1}{4} (\log (3-x)-\log (x+1)+4 c_1)\right )-1 \\ y(x)\to -2 \\ y(x)\to 0 \\ y(x)\to \text {Interval}[\{-3,1\}]+i \text {Interval}\left [\left \{-\sqrt {3},\sqrt {3}\right \}\right ] \\ \end{align*}