44.6.45 problem 45

Internal problem ID [7189]
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 : 45
Date solved : Tuesday, February 04, 2025 at 12:45:57 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+y \,{\mathrm e}^{x}&=1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 24

dsolve([diff(y(x),x)+exp(x)*y(x)=1,y(0) = 1],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-{\mathrm e}^{x}} \left (-\operatorname {Ei}_{1}\left (-{\mathrm e}^{x}\right )+\operatorname {Ei}_{1}\left (-1\right )+{\mathrm e}\right ) \]

✓ Solution by Mathematica

Time used: 0.056 (sec). Leaf size: 23

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

\[ y(x)\to e^{-e^x} \left (\operatorname {ExpIntegralEi}\left (e^x\right )-\operatorname {ExpIntegralEi}(1)+e\right ) \]