Internal problem ID [12870]
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: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=-3 t^{2}+2 t +3} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 26
dsolve([diff(y(t),t$2)+4*y(t)=-3*t^2+2*t+3,y(0) = 2, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sin \left (2 t \right )}{4}+\frac {7 \cos \left (2 t \right )}{8}-\frac {3 t^{2}}{4}+\frac {t}{2}+\frac {9}{8} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 31
DSolve[{y''[t]+4*y[t]==-3*t^2+2*t+3,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{8} \left (-6 t^2+4 t-2 \sin (2 t)-9 \cos (2 t)+9\right ) \]