56.1.83 problem 82

Internal problem ID [8795]
Book : Own collection of miscellaneous problems
Section : section 1.0
Problem number : 82
Date solved : Monday, January 27, 2025 at 05:00:50 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} z^{\prime \prime }+3 z^{\prime }+2 z&=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

dsolve(diff(z(t),t$2)+3*diff(z(t),t)+2*z(t)=24*(exp(-3*t)-exp(-4*t)),z(t), singsol=all)
 

\[ z = \left (-{\mathrm e}^{-t} c_{1} -4 \,{\mathrm e}^{-3 t}+12 \,{\mathrm e}^{-2 t}+c_{2} \right ) {\mathrm e}^{-t} \]

✓ Solution by Mathematica

Time used: 0.190 (sec). Leaf size: 34

DSolve[D[z[t],{t,2}]+3*D[z[t],t]+2*z[t]==24*(Exp[-3*t]-Exp[-4*t]),z[t],t,IncludeSingularSolutions -> True]
 

\[ z(t)\to e^{-4 t} \left (12 e^t+c_1 e^{2 t}+c_2 e^{3 t}-4\right ) \]