Internal problem ID [14547]
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: 41.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+4 y^{\prime }=8 \,{\mathrm e}^{4 t}-4 \,{\mathrm e}^{-4 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(t),t$2)+4*diff(y(t),t)=8*exp(4*t)-4*exp(-4*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (4 t -c_{1} +1\right ) {\mathrm e}^{-4 t}}{4}+c_{2} +\frac {{\mathrm e}^{4 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.115 (sec). Leaf size: 31
DSolve[y''[t]+4*y'[t]==8*Exp[4*t]-4*Exp[-4*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} e^{-4 t} \left (4 t+e^{8 t}+1-c_1\right )+c_2 \]