Internal problem ID [5808]
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]
\[ \boxed {\left (-2+2 y\right ) y^{\prime }=-2 x -3} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 43
dsolve((2*x+3)+(2*y(x)-2)*diff(y(x),x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 1-\sqrt {-x^{2}-c_{1} -3 x +1} y \left (x \right ) = 1+\sqrt {-x^{2}-c_{1} -3 x +1} \end{align*}
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 51
DSolve[(2*x+3)+(2*y[x]-2)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1-\sqrt {-x^2-3 x+1+2 c_1} y(x)\to 1+\sqrt {-x^2-3 x+1+2 c_1} \end{align*}