Internal problem ID [12865]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=2 \,{\mathrm e}^{-2 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve([diff(y(t),t$2)+4*y(t)=2*exp(-2*t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sin \left (2 t \right )}{4}-\frac {\cos \left (2 t \right )}{4}+\frac {{\mathrm e}^{-2 t}}{4} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 25
DSolve[{y''[t]+4*y[t]==2*Exp[-2*t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} \left (e^{-2 t}+\sin (2 t)-\cos (2 t)\right ) \]