Internal problem ID [13127]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 3. Linear Systems. Exercises section 3.6 page 342
Problem number: 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-12 y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 17
dsolve(diff(y(t),t$2)-diff(y(t),t)-12*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = \left ({\mathrm e}^{7 t} c_{2} +c_{1} \right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 22
DSolve[y''[t]-y'[t]-12*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-3 t} \left (c_2 e^{7 t}+c_1\right ) \]