10.7.22 problem 24

Internal problem ID [1270]
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 : 24
Date solved : Monday, January 27, 2025 at 04:48:32 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }+\left (3-\alpha \right ) y^{\prime }-2 \left (\alpha -1\right ) y&=0 \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$2) +(3-alpha)*diff(y(x),x)-2*(alpha-1)*y(x) = 0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x} c_1 +c_2 \,{\mathrm e}^{\left (\alpha -1\right ) x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 24

DSolve[D[y[x],{x,2}]+(3-\[Alpha])*D[y[x],x]-2*(\[Alpha]-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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