Internal problem ID [2015]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 15, Higher order ordinary differential equations. 15.4 Exercises, page
523
Problem number: Problem 15.23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {\left (-2+x \right ) y^{\prime \prime }+3 y^{\prime }+\frac {4 y}{x^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 30
dsolve((x-2)*diff(y(x),x$2)+3*diff(y(x),x)+4*y(x)/x^2=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (3 x -4\right ) c_{1}}{x \left (-2+x \right )^{2}}+\frac {x^{2} c_{2}}{\left (-2+x \right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 44
DSolve[(x-2)*y''[x]+3*y'[x]+4*y[x]/x^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {6 c_1 x^3+c_2 (3 x-4)}{6 \sqrt {2-x} (x-2)^{3/2} x} \\ \end{align*}