12.18.6 problem section 9.2, problem 6

Internal problem ID [2120]
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 6
Date solved : Monday, January 27, 2025 at 05:42:37 AM
CAS classification : [[_3rd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

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

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

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