Internal problem ID [14701]
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: 26.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }=3 t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 28
dsolve([diff(y(t),t$3)-diff(y(t),t$2)=3*t^2,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 6 \,{\mathrm e}^{t}-3 t^{2}-t^{3}-\frac {t^{4}}{4}-6 t -6 \]
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 32
DSolve[{y'''[t]-y''[t]==3*t^2,{y[0]==0,y'[0]==0,y''[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\frac {t^4}{4}-t^3-3 t^2-6 t+6 e^t-6 \]