Internal problem ID [14852]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-6 y^{\prime }+13 y=3 \,{\mathrm e}^{-2 t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)-6*diff(y(t),t)+13*y(t)=3*exp(-2*t),y(t), singsol=all)
\[ y \left (t \right ) = \left (\cos \left (2 t \right ) c_{1} +\sin \left (2 t \right ) c_{2} \right ) {\mathrm e}^{-2 t} {\mathrm e}^{5 t}+\frac {3 \,{\mathrm e}^{-2 t}}{29} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 39
DSolve[y''[t]-6*y'[t]+13*y[t]==3*Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {3 e^{-2 t}}{29}+c_2 e^{3 t} \cos (2 t)+c_1 e^{3 t} \sin (2 t) \]