Internal problem ID [12862]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }+10 y=10} \] 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: 26
dsolve([diff(y(t),t$2)+2*diff(y(t),t)+10*y(t)=10,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 1+\frac {\left (-3 \cos \left (3 t \right )-\sin \left (3 t \right )\right ) {\mathrm e}^{-t}}{3} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 32
DSolve[{y''[t]+2*y'[t]+10*y[t]==10,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^{-t} \left (3 e^t-\sin (3 t)-3 \cos (3 t)\right ) \]