Internal problem ID [14671]
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: 59.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+12 y^{\prime \prime \prime }+60 y^{\prime \prime }+124 y^{\prime }+75 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(t),t$4)+12*diff(y(t),t$3)+60*diff(y(t),t$2)+124*diff(y(t),t)+75*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{-3 t}+c_{2} {\mathrm e}^{-t}+c_{3} {\mathrm e}^{-4 t} \sin \left (3 t \right )+c_{4} {\mathrm e}^{-4 t} \cos \left (3 t \right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 40
DSolve[y''''[t]+12*y'''[t]+60*y''[t]+124*y'[t]+75*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-4 t} \left (c_3 e^t+c_4 e^{3 t}+c_2 \cos (3 t)+c_1 \sin (3 t)\right ) \]