15.9.9 problem 23

Internal problem ID [3066]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 17, page 78
Problem number : 23
Date solved : Monday, January 27, 2025 at 07:19:05 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

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

\[ y = c_{1} {\mathrm e}^{\frac {\left (3+\sqrt {5}\right ) x}{2}}+c_2 \,{\mathrm e}^{-\frac {\left (\sqrt {5}-3\right ) x}{2}} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 35

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

\[ y(x)\to e^{-\frac {1}{2} \left (\sqrt {5}-3\right ) x} \left (c_2 e^{\sqrt {5} x}+c_1\right ) \]