Internal problem ID [12852]
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: 12.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+7 y^{\prime }+10 y={\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 22
dsolve([diff(y(t),t$2)+7*diff(y(t),t)+10*y(t)=exp(-2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (3 t -1\right ) {\mathrm e}^{-2 t}}{9}+\frac {{\mathrm e}^{-5 t}}{9} \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 27
DSolve[{y''[t]+7*y'[t]+10*y[t]==Exp[-2*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{9} e^{-5 t} \left (e^{3 t} (3 t-1)+1\right ) \]