Internal problem ID [14663]
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: 44.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {24 y^{\prime \prime \prime }-26 y^{\prime \prime }+9 y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve([24*diff(y(t),t$3)-26*diff(y(t),t$2)+9*diff(y(t),t)-y(t)=0,y(0) = 0, D(y)(0) = 1, (D@@2)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 54 \,{\mathrm e}^{\frac {t}{3}}-14 \,{\mathrm e}^{\frac {t}{2}}-40 \,{\mathrm e}^{\frac {t}{4}} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 33
DSolve[{24*y'''[t]-26*y''[t]+9*y'[t]-y[t]==0,{y[0]==0,y'[0]==1,y''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -40 e^{t/4}+54 e^{t/3}-14 e^{t/2} \]