Internal problem ID [469]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {-y+2 y^{\prime }-{\mathrm e}^{\frac {t}{3}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = a] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve([-y(t)+2*diff(y(t),t) = exp(1/3*t),y(0) = a],y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{\frac {t}{3}} \left (-3+\left (a +3\right ) {\mathrm e}^{\frac {t}{6}}\right ) \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 26
DSolve[{-y[t]+2*y'[t] == Exp[1/3*t],y[0]==a},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{t/3} \left ((a+3) e^{t/6}-3\right ) \\ \end{align*}