Internal problem ID [12922]
Book: DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th
edition. Brooks/Cole. Boston, USA. 2012
Section: Chapter 6. Laplace transform. Section 6.6. page 624
Problem number: 8.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+16 y=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 18
dsolve([diff(y(t),t$2)+16*y(t)=t,y(0) = 1, D(y)(0) = 1],y(t), singsol=all)
\[ y = \frac {t}{16}+\cos \left (4 t \right )+\frac {15 \sin \left (4 t \right )}{64} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 24
DSolve[{y''[t]+16*y[t]==t,{y[0]==1,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{64} (4 t+15 \sin (4 t))+\cos (4 t) \]