Internal problem ID [619]
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: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\left (2 \alpha -1\right ) y^{\prime }+\alpha \left (-1+\alpha \right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve(diff(y(x),x$2) -(2*alpha-1)*diff(y(x),x)+alpha*(alpha-1)*y(x) = 0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{\alpha x}+c_{2} {\mathrm e}^{\left (\alpha -1\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 24
DSolve[y''[x]-(2*\[Alpha]-1)*y'[x]+\[Alpha]*(\[Alpha]-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^{(\alpha -1) x}+c_2 e^{\alpha x} \\ \end{align*}