Internal problem ID [689]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page
190
Problem number: 7.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y^{\prime }+4 y-\frac {{\mathrm e}^{-2 t}}{t^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.01 (sec). Leaf size: 28
dsolve(diff(y(t),t$2)+4*diff(y(t),t)+4*y(t) = t^(-2)*exp(-2*t),y(t), singsol=all)
\[ y \relax (t ) = {\mathrm e}^{-2 t} c_{2}+{\mathrm e}^{-2 t} t c_{1}-\left (\ln \relax (t )+1\right ) {\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.011 (sec). Leaf size: 23
DSolve[y''[t]+4*y'[t]+4*y[t] == t^(-2)*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-2 t} (-\log (t)+c_2 t-1+c_1) \\ \end{align*}