Internal problem ID [4472]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {-2 y-y^{2}}+\left (-x^{2}+2 x +3\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = -1+\sin \left (\frac {\ln \left (x -3\right )}{4}-\frac {\ln \left (x +1\right )}{4}+c_{1}\right ) \]
✓ Solution by Mathematica
Time used: 60.318 (sec). Leaf size: 369
DSolve[Sqrt[-2*y[x]-y[x]^2]+(3+2*x-x^2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1-\frac {1}{4} \sqrt {8-e^{-4 i c_1} (-((x-3) (x+1)))^{-i} \sqrt {e^{4 i c_1} (-((x-3) (x+1)))^i \left ((x+1)^i+16 e^{4 i c_1} (3-x)^i\right ){}^2}} \\ y(x)\to \frac {1}{4} \left (-4+\sqrt {8-e^{-4 i c_1} (-((x-3) (x+1)))^{-i} \sqrt {e^{4 i c_1} (-((x-3) (x+1)))^i \left ((x+1)^i+16 e^{4 i c_1} (3-x)^i\right ){}^2}}\right ) \\ y(x)\to \frac {1}{4} \left (-4-\sqrt {8+e^{-4 i c_1} (-((x-3) (x+1)))^{-i} \sqrt {e^{4 i c_1} (-((x-3) (x+1)))^i \left ((x+1)^i+16 e^{4 i c_1} (3-x)^i\right ){}^2}}\right ) \\ y(x)\to \frac {1}{4} \left (-4+\sqrt {8+e^{-4 i c_1} (-((x-3) (x+1)))^{-i} \sqrt {e^{4 i c_1} (-((x-3) (x+1)))^i \left ((x+1)^i+16 e^{4 i c_1} (3-x)^i\right ){}^2}}\right ) \\ \end{align*}