Internal problem ID [14660]
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: 41.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 36
dsolve([diff(y(t),t$3)-y(t)=0,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{t}-\sqrt {3}\, {\mathrm e}^{-\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right )-{\mathrm e}^{-\frac {t}{2}} \cos \left (\frac {\sqrt {3}\, t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 52
DSolve[{y'''[t]-y[t]==0,{y[0]==0,y'[0]==0,y''[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t/2} \left (e^{3 t/2}-\sqrt {3} \sin \left (\frac {\sqrt {3} t}{2}\right )-\cos \left (\frac {\sqrt {3} t}{2}\right )\right ) \]