Internal problem ID [12878]
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: 40.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+6 y^{\prime }+8 y=2 t +{\mathrm e}^{t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve([diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=2*t+exp(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (16 \,{\mathrm e}^{5 t}+60 t \,{\mathrm e}^{4 t}-45 \,{\mathrm e}^{4 t}+20 \,{\mathrm e}^{2 t}+9\right ) {\mathrm e}^{-4 t}}{240} \]
✓ Solution by Mathematica
Time used: 0.2 (sec). Leaf size: 33
DSolve[{y''[t]+6*y'[t]+8*y[t]==2*t+Exp[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{240} \left (60 t+9 e^{-4 t}+20 e^{-2 t}+16 e^t-45\right ) \]