Internal problem ID [14650]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.5, page 175
Problem number: 31.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+7 y^{\prime \prime \prime }+6 y^{\prime \prime }-32 y^{\prime }-32 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$4)+7*diff(y(t),t$3)+6*diff(y(t),t$2)-32*diff(y(t),t)-32*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left (c_{2} {\mathrm e}^{6 t}+c_{1} {\mathrm e}^{3 t}+t c_{4} +c_{3} \right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 34
DSolve[y''''[t]+7*y'''[t]+6*y''[t]-32*y'[t]-32*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-4 t} \left (c_2 t+c_3 e^{3 t}+c_4 e^{6 t}+c_1\right ) \]