Internal problem ID [674]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Chapter 3, Second order linear equations, 3.4 Repeated roots, reduction of order , page
172
Problem number: 28.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (x -1\right ) y^{\prime \prime }-y^{\prime } x +y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{x} \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 12
dsolve([(x-1)*diff(y(x),x$2)-x*diff(y(x),x)+y(x)=0,exp(x)],y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.019 (sec). Leaf size: 17
DSolve[(x-1)*y''[x]-x*y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 e^x-c_2 x \\ \end{align*}