Internal problem ID [14510]
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: 39.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {a y^{\prime \prime }+2 b y^{\prime }+c y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(a*diff(y(t),t$2)+2*b*diff(y(t),t)+c*y(t)=0,y(t), singsol=all)
\[ y \left (t \right ) = c_{1} {\mathrm e}^{\frac {\left (-b +\sqrt {-a c +b^{2}}\right ) t}{a}}+c_{2} {\mathrm e}^{-\frac {\left (b +\sqrt {-a c +b^{2}}\right ) t}{a}} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 54
DSolve[a*y''[t]+2*b*y'[t]+c*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-\frac {t \left (\sqrt {b^2-a c}+b\right )}{a}} \left (c_2 e^{\frac {2 t \sqrt {b^2-a c}}{a}}+c_1\right ) \]