Internal problem ID [12846]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 4. Forcing and Resonance. Section 4.1 page 399
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+10 y={\mathrm e}^{-2 t}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)+7*diff(y(t),t)+10*y(t)=exp(-2*t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} {\mathrm e}^{-5 t}+c_{1} {\mathrm e}^{-2 t}+\frac {t \,{\mathrm e}^{-2 t}}{3} \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 31
DSolve[y''[t]+7*y'[t]+10*y[t]==Exp[-2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-5 t} \left (e^{3 t} \left (\frac {t}{3}-\frac {1}{9}+c_2\right )+c_1\right ) \]