Internal problem ID [14127]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 1 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }-y=\frac {1}{1-t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(t),t)=y(t)+1/(1-t),y(t), singsol=all)
\[ y \left (t \right ) = \left ({\mathrm e}^{-1} \operatorname {expIntegral}_{1}\left (t -1\right )+c_{1} \right ) {\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 24
DSolve[y'[t]==y[t]+1/(1-t),y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{t-1} (-\operatorname {ExpIntegralEi}(1-t)+e c_1) \]