Internal problem ID [5741]
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]
\[ \boxed {\left (x +2 y\right ) y^{\prime }=1} \] With initial conditions \begin {align*} [y \left (0\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 9
dsolve([(x+2*y(x))*diff(y(x),x)=1,y(0) = -1],y(x), singsol=all)
\[ y \left (x \right ) = -\frac {x}{2}-1 \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 12
DSolve[{(x+2*y[x])*y'[x]==1,{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{2}-1 \]