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]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y=0} \] 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: 25
dsolve([(1-x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=0,x],singsol=all)
\[ y \left (x \right ) = \frac {c_{2} \ln \left (x -1\right ) x}{2}-\frac {c_{2} \ln \left (x +1\right ) x}{2}+c_{1} x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 33
DSolve[(1-x^2)*y''[x]-2*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x-\frac {1}{2} c_2 (x \log (1-x)-x \log (x+1)+2) \]