7.9.4 problem 16

Internal problem ID [252]
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 : 16
Date solved : Monday, January 27, 2025 at 02:42:56 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+8 y^{\prime }-4 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

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

dsolve([diff(y(x),x$3)-5*diff(y(x),x$2)+8*diff(y(x),x)-4*y(x)=0,y(0) = 1, D(y)(0) = 4, (D@@2)(y)(0) = 0],y(x), singsol=all)
 

\[ y = \left (-10 x +13\right ) {\mathrm e}^{2 x}-12 \,{\mathrm e}^{x} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to -e^x \left (e^x (10 x-13)+12\right ) \]