Internal problem ID [14491]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.2, page 147
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-12 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = 7] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+diff(y(t),t)-12*y(t)=0,y(0) = 3, D(y)(0) = 7],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (19 \,{\mathrm e}^{7 t}+2\right ) {\mathrm e}^{-4 t}}{7} \]
✓ Solution by Mathematica
Time used: 0.017 (sec). Leaf size: 23
DSolve[{y''[t]+y'[t]-12*y[t]==0,{y[0]==3,y'[0]==7}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{7} e^{-4 t} \left (19 e^{7 t}+2\right ) \]