1.29 problem 29

Internal problem ID [4989]

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: 29.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }+y-2 x -1=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve(diff(y(x),x)+y(x)=2*x+1,y(x), singsol=all)
 

\[ y \relax (x ) = 2 x -1+{\mathrm e}^{-x} c_{1} \]

Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 18

DSolve[y'[x]+y[x]==2*x+1,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 2 x+c_1 e^{-x}-1 \\ \end{align*}