10.7.4 problem 4

Internal problem ID [1252]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, 3.1 Homogeneous Equations with Constant Coefficients, page 144
Problem number : 4
Date solved : Monday, January 27, 2025 at 04:47:54 AM
CAS classification : [[_2nd_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

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

\[ y = {\mathrm e}^{x} c_1 +c_2 \,{\mathrm e}^{\frac {x}{2}} \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 35

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

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