Internal problem ID [12874]
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: 35.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=t -\frac {1}{20} t^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve([diff(y(t),t$2)+4*y(t)=t-t^2/20,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sin \left (2 t \right )}{8}-\frac {\cos \left (2 t \right )}{160}-\frac {t^{2}}{80}+\frac {t}{4}+\frac {1}{160} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 31
DSolve[{y''[t]+4*y[t]==t-t^2/20,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{160} \left (-2 t^2+40 t-20 \sin (2 t)-\cos (2 t)+1\right ) \]