Internal problem ID [14503]
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: 30.
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 ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(t),t$2)-diff(y(t),t)+y(t)=0,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \sqrt {3}\, {\mathrm e}^{\frac {t}{2}} \sin \left (\frac {\sqrt {3}\, t}{2}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 30
DSolve[{y''[t]-y'[t]+y[t]==0,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {2 e^{t/2} \sin \left (\frac {\sqrt {3} t}{2}\right )}{\sqrt {3}} \]