Internal problem ID [13852]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y=t^{3}} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 4.188 (sec). Leaf size: 25
dsolve([diff(y(t),t$2)-4*y(t)=t^3,y(0) = 1, D(y)(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {3 t}{8}-\frac {t^{3}}{4}+\frac {19 \,{\mathrm e}^{2 t}}{32}+\frac {13 \,{\mathrm e}^{-2 t}}{32} \]
✓ Solution by Mathematica
Time used: 0.02 (sec). Leaf size: 34
DSolve[{y''[t]-4*y[t]==t^3,{y[0]==1,y'[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{32} \left (-4 t \left (2 t^2+3\right )-11 e^{-2 t}+43 e^{2 t}\right ) \]