Internal problem ID [470]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {-2 y+3 y^{\prime }-{\mathrm e}^{-\frac {\pi t}{2}}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = a] \end {align*}
✓ Solution by Maple
Time used: 0.014 (sec). Leaf size: 38
dsolve([-2*y(t)+3*diff(y(t),t) = exp(-1/2*Pi*t),y(0) = a],y(t), singsol=all)
\[ y \relax (t ) = \frac {\left (3 \pi a -2 \,{\mathrm e}^{-\frac {1}{2} \pi t -\frac {2}{3} t}+4 a +2\right ) {\mathrm e}^{\frac {2 t}{3}}}{3 \pi +4} \]
✓ Solution by Mathematica
Time used: 0.088 (sec). Leaf size: 43
DSolve[{-2*y[t]+3*y'[t] == Exp[-1/2*Pi*t],y[0]==a},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {e^{2 t/3} \left ((4+3 \pi ) a-2 e^{-\frac {1}{6} (4+3 \pi ) t}+2\right )}{4+3 \pi } \\ \end{align*}