7.9.2 problem 14

Internal problem ID [250]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.2 (General solutions of linear equations). Problems at page 122
Problem number : 14
Date solved : Monday, January 27, 2025 at 02:42:56 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 21

dsolve([diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=0,y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 3],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 19

DSolve[{D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==0,{y[0]==0,Derivative[1][y][0] ==0,Derivative[2][y][0] ==3}},y[x],x,IncludeSingularSolutions -> True]
 

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