Internal problem ID [14664]
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: 45.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 3, y^{\prime \prime }\left (0\right ) = -7, y^{\prime \prime \prime }\left (0\right ) = 15] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 15
dsolve([diff(y(t),t$4)-5*diff(y(t),t$2)+4*y(t)=0,y(0) = -1, D(y)(0) = 3, (D@@2)(y)(0) = -7, (D@@3)(y)(0) = 15],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-t}-2 \,{\mathrm e}^{-2 t} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 16
DSolve[{y''''[t]-5*y''[t]+4*y[t]==0,{y[0]==-1,y'[0]==3,y''[0]==-7,y'''[0]==15}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-2 t} \left (e^t-2\right ) \]