Internal problem ID [11705]
Book: AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C.
ROBINSON. Cambridge University Press 2004
Section: Chapter 12, Homogeneous second order linear equations. Exercises page 118
Problem number: 12.1 (xii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 16
dsolve([diff(y(t),t$2)+diff(y(t),t)-2*y(t)=0,y(0) = 4, D(y)(0) = -4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {4 \left ({\mathrm e}^{3 t}+2\right ) {\mathrm e}^{-2 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 21
DSolve[{y''[t]+y'[t]-2*y[t]==0,{y[0]==4,y'[0]==-4}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {4}{3} e^{-2 t} \left (e^{3 t}+2\right ) \]