65.4.4 problem 9.1 (iv)

Internal problem ID [13734]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 9, First order linear equations and the integrating factor. Exercises page 86
Problem number : 9.1 (iv)
Date solved : Tuesday, January 28, 2025 at 06:00:14 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.111 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 32

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

\[ y(x)\to e^{e^{-x}} \left (\int _0^xe^{-e^{-K[1]}}dK[1]+1\right ) \]