Internal problem ID [460]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {-y+y^{\prime }-2 \,{\mathrm e}^{2 t} t=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 16
dsolve([-y(t)+diff(y(t),t) = 2*exp(2*t)*t,y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \left (2 t -2\right ) {\mathrm e}^{2 t}+3 \,{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.06 (sec). Leaf size: 19
DSolve[{-y[t]+y'[t] == 2*Exp[2*t]*t,y[0]==1},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \left (2 e^t (t-1)+3\right ) \\ \end{align*}