44.2.45 problem 47

Internal problem ID [6977]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 47
Date solved : Monday, January 27, 2025 at 02:39:33 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&={\frac {1}{2}} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 15

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

\[ y = \frac {x}{2}-\frac {1}{4}+\frac {3 \,{\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 21

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

\[ y(x)\to \frac {1}{4} \left (2 x+3 e^{-2 x}-1\right ) \]