73.18.2 problem 27.1 (b)

Internal problem ID [15586]
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 (b)
Date solved : Tuesday, January 28, 2025 at 08:02:51 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=t^{3} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 8.707 (sec). Leaf size: 25

dsolve([diff(y(t),t)-2*y(t)=t^3,y(0) = 4],y(t), singsol=all)
 

\[ y = -\frac {3 t^{2}}{4}-\frac {t^{3}}{2}-\frac {3 t}{4}+\frac {35 \,{\mathrm e}^{2 t}}{8}-\frac {3}{8} \]

✓ Solution by Mathematica

Time used: 0.072 (sec). Leaf size: 31

DSolve[{D[y[t],t]+4*y[t]==t^3,{y[0]==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} \left (\int _0^te^{4 K[1]} K[1]^3dK[1]+4\right ) \]