7.9.6 problem 18

Internal problem ID [254]
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 : 18
Date solved : Wednesday, February 05, 2025 at 03:06:19 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-2 y&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

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

\[ y(x)\to -e^x (\sin (x)+\cos (x)-2) \]