9.2.16 problem problem 28

Internal problem ID [950]
Book : Differential equations and linear algebra, 4th ed., Edwards and Penney
Section : Section 5.3, Higher-Order Linear Differential Equations. Homogeneous Equations with Constant Coefficients. Page 300
Problem number : problem 28
Date solved : Monday, January 27, 2025 at 03:22:37 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \left (c_1 \,{\mathrm e}^{3 x}+c_2 \,{\mathrm e}^{\frac {x}{2}}+c_3 \right ) {\mathrm e}^{-x} \]

✓ Solution by Mathematica

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

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

\[ y(x)\to e^{-x} \left (c_1 e^{x/2}+c_3 e^{3 x}+c_2\right ) \]