Internal problem ID [14557]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.3, page 156
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+8 y^{\prime }+16 y=4} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {5}{4}}, y^{\prime }\left (0\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve([diff(y(t),t$2)+8*diff(y(t),t)+16*y(t)=4,y(0) = 5/4, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = {\mathrm e}^{-4 t}+4 t \,{\mathrm e}^{-4 t}+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 20
DSolve[{y''[t]+8*y'[t]+16*y[t]==4,{y[0]==5/4,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-4 t} (4 t+1)+\frac {1}{4} \]