12.18.18 problem section 9.2, problem 18

Internal problem ID [2132]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 18
Date solved : Monday, January 27, 2025 at 05:42:42 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=6\\ y^{\prime }\left (0\right )&=3\\ y^{\prime \prime }\left (0\right )&=22 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 25

dsolve([diff(y(x),x$3)-2*diff(y(x),x)-4*y(x)=0,y(0) = 6, D(y)(0) = 3, (D@@2)(y)(0) = 22],y(x), singsol=all)
 

\[ y = \left (-3 \sin \left (x \right )+2 \cos \left (x \right )\right ) {\mathrm e}^{-x}+4 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

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

DSolve[{D[y[x],{x,3}]-2*D[y[x],x]-4*y[x]==0,{y[0]==6,Derivative[1][y][0] ==3,Derivative[2][y][0] ==22}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (4 e^{3 x}-3 \sin (x)+2 \cos (x)\right ) \]