Internal problem ID [14564]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 58.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }={\mathrm e}^{-3 t}-{\mathrm e}^{3 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)-3*diff(y(t),t)=exp(-3*t)-exp(3*t),y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {4}{9}+\frac {\left (3-2 t \right ) {\mathrm e}^{3 t}}{6}+\frac {{\mathrm e}^{-3 t}}{18} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 27
DSolve[{y''[t]-3*y'[t]==Exp[-3*t]-Exp[3*t],{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{18} \left (e^{3 t} (9-6 t)+e^{-3 t}+8\right ) \]