Internal problem ID [4988]
Book: Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold
Scientific. Singapore. 1995
Section: Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page
7
Problem number: 28.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], [_Abel, 2nd type, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (x +2 y\right ) y^{\prime }-1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 9
dsolve([(x+2*y(x))*diff(y(x),x)=1,y(0) = -1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2}-1 \]
✓ Solution by Mathematica
Time used: 0.037 (sec). Leaf size: 12
DSolve[{(x+2*y[x])*y'[x]==1,{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x}{2}-1 \\ \end{align*}