Internal problem ID [13189]
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: 30.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+2 y=-{\mathrm e}^{t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 28
dsolve([diff(y(t),t$2)+2*y(t)=-exp(t),y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {\sqrt {2}\, \sin \left (\sqrt {2}\, t \right )}{6}+\frac {\cos \left (\sqrt {2}\, t \right )}{3}-\frac {{\mathrm e}^{t}}{3} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 39
DSolve[{y''[t]+2*y[t]==-Exp[t],{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{6} \left (-2 e^t+\sqrt {2} \sin \left (\sqrt {2} t\right )+2 \cos \left (\sqrt {2} t\right )\right ) \]