Internal problem ID [13544]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 28. The inverse Laplace transform. Additional Exercises. page 509
Problem number: 28.6 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=27 t^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 19
dsolve([diff(y(t),t$2)+9*y(t)=27*t^3,y(0) = 0, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = 3 t^{3}-2 t +\frac {2 \sin \left (3 t \right )}{3} \]
✓ Solution by Mathematica
Time used: 0.015 (sec). Leaf size: 22
DSolve[{y''[t]+9*y[t]==27*t^3,{y[0]==0,y'[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 3 t^3-2 t+\frac {2}{3} \sin (3 t) \]