Internal problem ID [4350]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page
435
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{2} \left (2-x \right ) y^{\prime \prime }+2 y^{\prime } x -2 y=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: 16
dsolve([x^2*(2-x)*diff(y(x),x$2)+2*x*diff(y(x),x)-2*y(x)=0,x],y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +\frac {c_{2} \left (x -1\right )}{x} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 24
DSolve[x^2*(2-x)*y''[x]+2*x*y'[x]-2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {c_1 (x-2)^2+c_2 (x-1)}{x} \\ \end{align*}