Internal problem ID [14497]
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: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 4, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 11
dsolve([diff(y(t),t$2)-2*diff(y(t),t)+y(t)=0,y(0) = 4, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -4 \,{\mathrm e}^{t} \left (t -1\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 13
DSolve[{y''[t]-2*y'[t]+y[t]==0,{y[0]==4,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -4 e^t (t-1) \]