12.18.4 problem section 9.2, problem 4

Internal problem ID [2118]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.2. constant coefficient. Page 483
Problem number : section 9.2, problem 4
Date solved : Monday, January 27, 2025 at 05:42:36 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \left (c_1 \,{\mathrm e}^{\frac {5 x}{2}}+c_2 \,{\mathrm e}^{\frac {x}{2}}+c_3 \right ) {\mathrm e}^{-\frac {3 x}{2}} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

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

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