Internal problem ID [14856]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 35.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-12 y^{\prime }-16 y={\mathrm e}^{4 t}-{\mathrm e}^{-2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(diff(y(t),t$3)-12*diff(y(t),t)-16*y(t)=exp(4*t)-exp(-2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (18 t^{2}+\left (216 c_{3} +6\right ) t +216 c_{1} +1\right ) {\mathrm e}^{-2 t}}{216}+\frac {\left (t +36 c_{2} -\frac {1}{3}\right ) {\mathrm e}^{4 t}}{36} \]
✓ Solution by Mathematica
Time used: 0.104 (sec). Leaf size: 49
DSolve[y'''[t]-12*y'[t]-16*y[t]==Exp[4*t]-Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{216} e^{-2 t} \left (18 t^2+6 (1+36 c_2) t+e^{6 t} (6 t-2+216 c_3)+1+216 c_1\right ) \]