67.4.38 problem Problem 13(b)

Internal problem ID [14082]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 5.6 Laplace transform. Nonhomogeneous equations. Problems page 368
Problem number : Problem 13(b)
Date solved : Tuesday, January 28, 2025 at 06:13:48 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-2 y^{\prime \prime }-y^{\prime }+2 y&=4 t \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=4 \end{align*}

✓ Solution by Maple

Time used: 7.661 (sec). Leaf size: 17

dsolve([diff(y(t),t$3)-2*diff(y(t),t$2)-diff(y(t),t)+2*y(t)=4*t,y(0) = 2, D(y)(0) = -2, (D@@2)(y)(0) = 4],y(t), singsol=all)
 

\[ y = -6 \sinh \left (t \right )+2 t +1+{\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 27

DSolve[{D[ y[t],{t,3}]-2*D[y[t],{t,2}]-D[y[t],t]+2*y[t]==4*t,{y[0]==2,Derivative[1][y][0] ==-2,Derivative[2][y][0] ==4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 t+3 e^{-t}-3 e^t+e^{2 t}+1 \]