3.3 problem 3

Internal problem ID [5055]

Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.3. Exact equations problems. page 24
Problem number: 3.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [_separable]

Solve \begin {gather*} \boxed {2 x +3+\left (2 y-2\right ) y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.015 (sec). Leaf size: 43

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

\begin{align*} y \relax (x ) = 1-\sqrt {-x^{2}-3 x -c_{1}+1} \\ y \relax (x ) = 1+\sqrt {-x^{2}-3 x -c_{1}+1} \\ \end{align*}

Solution by Mathematica

Time used: 0.183 (sec). Leaf size: 47

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

\begin{align*} y(x)\to 1-\sqrt {-x (x+3)+1+2 c_1} \\ y(x)\to 1+\sqrt {-x (x+3)+1+2 c_1} \\ \end{align*}