Internal problem ID [14461]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.1, page 141
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+10 y^{\prime }+25 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{-5 t} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve([diff(y(t),t$2)+10*diff(y(t),t)+25*y(t)=0,exp(-5*t)],singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-5 t} \left (c_{2} t +c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 18
DSolve[y''[t]+10*y'[t]+25*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-5 t} (c_2 t+c_1) \]