47.1.29 problem 29

Internal problem ID [7410]
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
Date solved : Monday, January 27, 2025 at 02:53:17 PM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 18

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

\[ y(x)\to 2 x+c_1 e^{-x}-1 \]