Internal problem ID [283]
Book: Differential equations and linear algebra, 4th ed., Edwards and Penney
Section: Section 5.2, Higher-Order Linear Differential Equations. General solutions of Linear
Equations. Page 288
Problem number: problem 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer]
Solve \begin {gather*} \boxed {\left (-x^{2}+1\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: 0.0 (sec). Leaf size: 26
dsolve([(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,x],y(x), singsol=all)
\[ y \relax (x ) = x c_{1}+c_{2} \left (\frac {x \ln \left (x -1\right )}{2}-\frac {x \ln \left (x +1\right )}{2}+1\right ) \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 19
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 x+c_2 \left (x \tanh ^{-1}(x)-1\right ) \\ \end{align*}