Internal problem ID [476]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.1. Page 40
Problem number: 29.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {\frac {y}{4}+y^{\prime }-3-2 \cos \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.008 (sec). Leaf size: 24
dsolve([1/4*y(t)+diff(y(t),t) = 3+2*cos(2*t),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = 12+\frac {8 \cos \left (2 t \right )}{65}+\frac {64 \sin \left (2 t \right )}{65}-\frac {788 \,{\mathrm e}^{-\frac {t}{4}}}{65} \]
✓ Solution by Mathematica
Time used: 0.1 (sec). Leaf size: 32
DSolve[{1/4*y[t]+y'[t] == 3+2*Cos[2*t],y[0]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {4}{65} \left (-197 e^{-t/4}+16 \sin (2 t)+2 \cos (2 t)+195\right ) \\ \end{align*}