13.10.2 problem 2

Internal problem ID [2403]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 2.4, The method of variation of parameters. Page 154
Problem number : 2
Date solved : Monday, January 27, 2025 at 05:51:45 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=t \,{\mathrm e}^{2 t} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

dsolve(diff(y(t),t$2)-4*diff(y(t),t)+4*y(t)=t*exp(2*t),y(t), singsol=all)
 

\[ y = {\mathrm e}^{2 t} \left (c_2 +c_1 t +\frac {1}{6} t^{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 27

DSolve[D[y[t],{t,2}]-4*D[y[t],t]+4*y[t]==t*Exp[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{6} e^{2 t} \left (t^3+6 c_2 t+6 c_1\right ) \]