Internal problem ID [7127]
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]]
\[ \boxed {z^{\prime \prime }+3 z^{\prime }+2 z=24 \,{\mathrm e}^{-3 t}-24 \,{\mathrm e}^{-4 t}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ z \left (t \right ) = \left (-{\mathrm e}^{-t} c_{1} -4 \,{\mathrm e}^{-3 t}+12 \,{\mathrm e}^{-2 t}+c_{2} \right ) {\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.084 (sec). Leaf size: 34
DSolve[z''[t]+3*z'[t]+2*z[t]==24*(Exp[-3*t]-Exp[-4*t]),z[t],t,IncludeSingularSolutions -> True]
\[ z(t)\to e^{-4 t} \left (12 e^t+c_1 e^{2 t}+c_2 e^{3 t}-4\right ) \]