44.6.27 problem 27

Internal problem ID [7171]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 27
Date solved : Tuesday, February 04, 2025 at 12:43:44 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }+y&={\mathrm e}^{x} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 16

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

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

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 28

DSolve[{D[y[x],x]+y[x]==Exp[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

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