47.1.28 problem 28

Internal problem ID [7409]
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
Date solved : Monday, January 27, 2025 at 02:53:15 PM
CAS classification : [[_homogeneous, `class C`], [_Abel, `2nd type`, `class C`], _dAlembert]

\begin{align*} \left (x +2 y\right ) y^{\prime }&=1 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 9

dsolve([(x+2*y(x))*diff(y(x),x)=1,y(0) = -1],y(x), singsol=all)
 

\[ y = -\frac {x}{2}-1 \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 12

DSolve[{(x+2*y[x])*D[y[x],x]==1,{y[0]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x}{2}-1 \]