14.16.7 problem 23

Internal problem ID [2677]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 2. Second order differential equations. Section 2.9, The method of Laplace transform. Excercises page 232
Problem number : 23
Date solved : Monday, January 27, 2025 at 06:06:17 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&={\mathrm e}^{4 t} \end{align*}

Using Laplace method With initial conditions

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

Solution by Maple

Time used: 0.853 (sec). Leaf size: 27

dsolve([diff(y(t),t$3)-6*diff(y(t),t$2)+11*diff(y(t),t)-6*y(t)=exp(4*t),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 0],y(t), singsol=all)
 
\[ y = -\frac {{\mathrm e}^{t}}{6}-\frac {{\mathrm e}^{3 t}}{2}+\frac {{\mathrm e}^{4 t}}{6}+\frac {{\mathrm e}^{2 t}}{2} \]

Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 19

DSolve[{D[y[t],{t,3}]-6*D[y[t],{t,2}]+11*D[y[t],t]-6*y[t]==Exp[4*t],{y[0]==0,Derivative[1][y][0] ==0,Derivative[2][y][0] ==0}},y[t],t,IncludeSingularSolutions -> True]
 
\[ y(t)\to \frac {1}{6} e^t \left (e^t-1\right )^3 \]