12.18.20 problem section 9.2, problem 20

Internal problem ID [2134]
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 20
Date solved : Monday, January 27, 2025 at 05:42:43 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+12 y^{\prime }-8 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

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

dsolve([diff(y(x),x$3)-6*diff(y(x),x$2)+12*diff(y(x),x)-8*y(x)=0,y(0) = 1, D(y)(0) = -1, (D@@2)(y)(0) = -4],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 21

DSolve[{D[y[x],{x,3}]-6*D[y[x],{x,2}]+12*D[y[x],x]-8*y[x]==0,{y[0]==1,Derivative[1][y][0] ==-1,Derivative[2][y][0] ==-4}},y[x],x,IncludeSingularSolutions -> True]
 

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