Internal problem ID [14705]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 30.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 1, y^{\prime \prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve([diff(y(t),t$4)+diff(y(t),t$2)=t,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 1, (D@@3)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {t^{3}}{6}-\cos \left (t \right )+\sin \left (t \right )-t +1 \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 23
DSolve[{y''''[t]+y''[t]==t,{y[0]==0,y'[0]==0,y''[0]==1,y'''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {t^3}{6}-t+\sin (t)-\cos (t)+1 \]