Internal problem ID [683]
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: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-5 y^{\prime }+6 y-2 \,{\mathrm e}^{t}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(t),t$2)-5*diff(y(t),t)+6*y(t) = 2*exp(t),y(t), singsol=all)
\[ y \relax (t ) = c_{2} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{2 t}+{\mathrm e}^{t} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 24
DSolve[y''[t]-5*y'[t]+6*y[t] == 2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^t \left (1+e^t \left (c_2 e^t+c_1\right )\right ) \\ \end{align*}