Internal problem ID [14501]
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: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+y^{\prime }-y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.046 (sec). Leaf size: 37
dsolve([diff(y(t),t$2)+diff(y(t),t)-y(t)=0,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (5+\sqrt {5}\right ) {\mathrm e}^{\frac {\left (\sqrt {5}-1\right ) t}{2}}}{10}-\frac {{\mathrm e}^{-\frac {\left (\sqrt {5}+1\right ) t}{2}} \left (-5+\sqrt {5}\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 49
DSolve[{y''[t]+y'[t]-y[t]==0,{y[0]==1,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{10} e^{-\frac {1}{2} \left (1+\sqrt {5}\right ) t} \left (\left (5+\sqrt {5}\right ) e^{\sqrt {5} t}+5-\sqrt {5}\right ) \]