78.1.47 problem 8

Internal problem ID [18102]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 11:26:22 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)
 

\[ y = \left (c_{3} {\mathrm e}^{3 x}+c_{1} {\mathrm e}^{\frac {5 x}{2}}+c_{2} \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

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

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]
 

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