10.10.1 problem 1

Internal problem ID [1333]
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
Date solved : Monday, January 27, 2025 at 04:51:15 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=2 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = c_2 \,{\mathrm e}^{3 t}+{\mathrm e}^{2 t} c_1 +{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 25

DSolve[D[y[t],{t,2}]-5*D[y[t],t]+6*y[t] == 2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^t \left (c_1 e^t+c_2 e^{2 t}+1\right ) \]