Internal problem ID [14695]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }-11 y^{\prime }+30 y={\mathrm e}^{4 t}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 32
dsolve(diff(y(t),t$3)-4*diff(y(t),t$2)-11*diff(y(t),t)+30*y(t)=exp(4*t),y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\left (-14 c_{3} {\mathrm e}^{8 t}+{\mathrm e}^{7 t}-14 c_{2} {\mathrm e}^{5 t}-14 c_{1} \right ) {\mathrm e}^{-3 t}}{14} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 39
DSolve[y'''[t]-4*y''[t]-11*y'[t]+30*y[t]==Exp[4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {e^{4 t}}{14}+c_1 e^{-3 t}+c_2 e^{2 t}+c_3 e^{5 t} \]