41.1.28 problem 28

Internal problem ID [8695]
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 : Tuesday, September 30, 2025 at 05:41:36 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*}

✓ Maple. Time used: 0.028 (sec). Leaf size: 9

ode:=(x+2*y(x))*diff(y(x),x) = 1; 
ic:=[y(0) = -1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.056 (sec). Leaf size: 52

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

\[ \text {Solve}\left [x=e^{y(x)} \int _0^{y(x)}2 e^{-K[1]} K[1]dK[1]-e^{y(x)} \int _0^{-1}2 e^{-K[1]} K[1]dK[1],y(x)\right ] \]

✓ Sympy. Time used: 0.575 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((x + 2*y(x))*Derivative(y(x), x) - 1,0) 
ics = {y(0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{2} - 1 \]