Internal problem ID [11706]
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 (xiii).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-4 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 10, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)-4*y(t)=0,y(0) = 10, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 5 \,{\mathrm e}^{-2 t}+5 \,{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 19
DSolve[{y''[t]-4*y[t]==0,{y[0]==10,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 5 e^{-2 t} \left (e^{4 t}+1\right ) \]