7.4 problem 4

Internal problem ID [1719]

Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.2, linear equations with constant coefficients. Page 138
Problem number: 4.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x]]

\[ \boxed {3 y^{\prime \prime }+6 y^{\prime }+3 y=0} \]

Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

dsolve(3*diff(y(t),t$2)+6*diff(y(t),t)+3*y(t)=0,y(t), singsol=all)
 

\[ y \left (t \right ) = {\mathrm e}^{-t} c_{1} +c_{2} {\mathrm e}^{-t} t \]

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 18

DSolve[3*y''[t]+6*y'[t]+3*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-t} (c_2 t+c_1) \]