7.9.1 problem 13

Internal problem ID [249]
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 : 13
Date solved : Monday, January 27, 2025 at 02:42:56 AM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=2\\ y^{\prime \prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 22

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

\[ y(x)\to \frac {4 e^x}{3}-\frac {1}{3} e^{-2 x} \]