13.10.4 problem 4

Internal problem ID [2405]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.4, The method of variation of parameters. Page 154
Problem number : 4
Date solved : Monday, January 27, 2025 at 05:51:49 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-3 y^{\prime }+2 y&=t \,{\mathrm e}^{3 t}+1 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(t),t$2)-3*diff(y(t),t)+2*y(t)=t*exp(3*t)+1,y(t), singsol=all)
 

\[ y = \frac {\left (2 t -3\right ) {\mathrm e}^{3 t}}{4}+{\mathrm e}^{2 t} c_1 +c_2 \,{\mathrm e}^{t}+\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 37

DSolve[D[y[t],{t,2}]-3*D[y[t],t]+2*y[t]==t*Exp[3*t]+1,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{4} e^{3 t} (2 t-3)+c_1 e^t+c_2 e^{2 t}+\frac {1}{2} \]