Internal problem ID [14260]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 31.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime } t +y=2 t \,{\mathrm e}^{t}} \] With initial conditions \begin {align*} [y \left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([t*diff(y(t),t)+y(t)=2*t*exp(t),y(1) = -1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {-1+\left (2 t -2\right ) {\mathrm e}^{t}}{t} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 19
DSolve[{t*y'[t]+y[t]==2*t*Exp[t],{y[1]==-1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2 e^t (t-1)-1}{t} \]