12.18.26 problem section 9.2, problem 26

Internal problem ID [2140]
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 26
Date solved : Monday, January 27, 2025 at 05:42:46 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+2 y^{\prime \prime \prime }-2 y^{\prime \prime }-8 y^{\prime }-8 y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=-2\\ y^{\prime \prime }\left (0\right )&=6\\ y^{\prime \prime \prime }\left (0\right )&=8 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 25

dsolve([diff(y(x),x$4)+2*diff(y(x),x$3)-2*diff(y(x),x$2)-8*diff(y(x),x)-8*y(x)=0,y(0) = 5, D(y)(0) = -2, (D@@2)(y)(0) = 6, (D@@3)(y)(0) = 8],y(x), singsol=all)
 

\[ y = \left (1+{\mathrm e}^{4 x}+\left (\sin \left (x \right )+3 \cos \left (x \right )\right ) {\mathrm e}^{x}\right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 31

DSolve[{D[y[x],{x,4}]+2*D[y[x],{x,3}]-2*D[y[x],{x,2}]-8*D[y[x],x]-8*y[x]==0,{y[0]==5,Derivative[1][y][0] ==-2,Derivative[2][y][0] ==6,Derivative[3][y][0]==8}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{4 x}+e^x \sin (x)+3 e^x \cos (x)+1\right ) \]