76.17.1 problem 10

Internal problem ID [17687]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 10:59:32 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)
 

\[ y = c_{2} {\mathrm e}^{3 t}+c_{1} {\mathrm e}^{2 t}+{\mathrm e}^{t} \]

✓ Solution by Mathematica

Time used: 0.015 (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]
 

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