Internal problem ID [11678]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+{\mathrm e}^{-x} y=1} \] With initial conditions \begin {align*} [y \left (0\right ) = {\mathrm e}] \end {align*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 23
dsolve([diff(y(x),x)+exp(-x)*y(x)=1,y(0) = exp(1)],y(x), singsol=all)
\[ y \left (x \right ) = -\left (-\operatorname {Ei}_{1}\left ({\mathrm e}^{-x}\right )-1+\operatorname {Ei}_{1}\left (1\right )\right ) {\mathrm e}^{{\mathrm e}^{-x}} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 27
DSolve[{y'[x]+Exp[-x]*y[x]==1,{y[0]==Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{e^{-x}} \left (-\operatorname {ExpIntegralEi}\left (-e^{-x}\right )+\operatorname {ExpIntegralEi}(-1)+1\right ) \]