12.18.22 problem section 9.2, problem 22

Internal problem ID [2136]
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 22
Date solved : Monday, January 27, 2025 at 05:42:44 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} 8 y^{\prime \prime \prime }-4 y^{\prime \prime }-2 y^{\prime }+y&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=4\\ y^{\prime }\left (0\right )&=-3\\ y^{\prime \prime }\left (0\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 22

dsolve([8*diff(y(x),x$3)-4*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=0,y(0) = 4, D(y)(0) = -3, (D@@2)(y)(0) = -1],y(x), singsol=all)
 

\[ y = 3 \,{\mathrm e}^{-\frac {x}{2}}+{\mathrm e}^{\frac {x}{2}}-2 x \,{\mathrm e}^{\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 57

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

\[ y(x)\to -\frac {2}{21} e^{-x/4} \left (9 e^{5 x/4}+13 \sqrt {3} \sin \left (\frac {\sqrt {3} x}{4}\right )-51 \cos \left (\frac {\sqrt {3} x}{4}\right )\right ) \]