Internal problem ID [6374]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 82.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {z^{\prime \prime }+3 z^{\prime }+2 z-24 \,{\mathrm e}^{-3 t}+24 \,{\mathrm e}^{-4 t}=0} \end {gather*}
✓ 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)
\[ z \relax (t ) = \left (-{\mathrm e}^{-t} c_{1}-4 \,{\mathrm e}^{-3 t}+12 \,{\mathrm e}^{-2 t}+c_{2}\right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 32
DSolve[z''[t]+3*z'[t]+2*z[t]==24*(Exp[-3*t]-Exp[-4*t]),z[t],t,IncludeSingularSolutions -> True]
\begin{align*} z(t)\to e^{-4 t} \left (-4+e^t \left (12+e^t \left (c_2 e^t+c_1\right )\right )\right ) \\ \end{align*}