Internal problem ID [13541]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page
496
Problem number: 27.1 (m).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime \prime }-27 y={\mathrm e}^{-3 t}} \] With initial conditions \begin {align*} [y \left (0\right ) = 2, y^{\prime }\left (0\right ) = 3, y^{\prime \prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 44
dsolve([diff(y(t),t$3)-27*y(t)=exp(-3*t),y(0) = 2, D(y)(0) = 3, (D@@2)(y)(0) = 4],y(t), singsol=all)
\[ y \left (t \right ) = \frac {14 \sqrt {3}\, {\mathrm e}^{-\frac {3 t}{2}} \sin \left (\frac {3 \sqrt {3}\, t}{2}\right )}{81}+\frac {70 \,{\mathrm e}^{-\frac {3 t}{2}} \cos \left (\frac {3 \sqrt {3}\, t}{2}\right )}{81}+\frac {92 \cosh \left (3 t \right )}{81}+\frac {95 \sinh \left (3 t \right )}{81} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y''[t]-27*y[t]==Exp[-3*t],{y[0]==4,y'[0]==3,y''[0]==4}},y[t],t,IncludeSingularSolutions -> True]
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