Internal problem ID [14676]
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: 1.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }={\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve(diff(y(t),t$3)+diff(y(t),t$2)=exp(t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {{\mathrm e}^{t}}{2}+{\mathrm e}^{-t} c_{1} +t c_{2} +c_{3} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 27
DSolve[y'''[t]+y''[t]==Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {e^t}{2}+c_1 e^{-t}+c_3 t+c_2 \]