Internal problem ID [5590]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.4. THE USE OF A KNOWN
SOLUTION TO FIND ANOTHER. Page 74
Problem number: 6(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {x y^{\prime }}{x -1}+\frac {y}{x -1}=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(x),x$2)-x/(x-1)*diff(y(x),x)+1/(x-1)*y(x)=0,x],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} {\mathrm e}^{x} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[y''[x]-x/(x-1)*x*y'[x]+1/(x-1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Not solved