14.11.6 problem 6

Internal problem ID [2599]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.5. Method of judicious guessing. Excercises page 164
Problem number : 6
Date solved : Monday, January 27, 2025 at 06:02:16 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+5 y^{\prime }+4 y&=t^{2} {\mathrm e}^{7 t} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 34

dsolve(diff(y(t),t$2)+5*diff(y(t),t)+4*y(t)=t^2*exp(7*t),y(t), singsol=all)
 

\[ y = \frac {{\mathrm e}^{-4 t} \left (\left (\frac {273}{3872}+t^{2}-\frac {19}{44} t \right ) {\mathrm e}^{11 t}+88 c_1 \,{\mathrm e}^{3 t}+88 c_2 \right )}{88} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 41

DSolve[D[y[t],{t,2}]+5*D[y[t],t]+4*y[t]==t^2*Exp[7*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{7 t} \left (3872 t^2-1672 t+273\right )}{340736}+c_1 e^{-4 t}+c_2 e^{-t} \]