11.2.10 problem 17

Internal problem ID [1481]
Book : Elementary differential equations and boundary value problems, 11th ed., Boyce, DiPrima, Meade
Section : Chapter 4.2, Higher order linear differential equations. Constant coefficients. page 180
Problem number : 17
Date solved : Monday, January 27, 2025 at 04:57:49 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }+5 y^{\prime \prime }+6 y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 32

dsolve(diff(y(x),x$3)+5*diff(y(x),x$2)+6*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-x} c_1 +c_2 \,{\mathrm e}^{\left (-2+\sqrt {2}\right ) x}+c_3 \,{\mathrm e}^{-\left (2+\sqrt {2}\right ) x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 43

DSolve[D[y[x],{x,3}]+5*D[y[x],{x,2}]+6*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (c_1 e^{-\left (\left (1+\sqrt {2}\right ) x\right )}+c_2 e^{\left (\sqrt {2}-1\right ) x}+c_3\right ) \]