Internal problem ID [13875]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 29. Convolution. Additional Exercises. page 523
Problem number: 29.6 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }+4 y=t} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.141 (sec). Leaf size: 14
dsolve([diff(y(t),t$2)+4*y(t)=t,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\sin \left (2 t \right )}{8}+\frac {t}{4} \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 17
DSolve[{y''[t]+4*y[t]==t,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} (t-\sin (t) \cos (t)) \]