Internal problem ID [2047]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }+y x -a x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2 a] \end {align*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 20
dsolve([(1-x^2)*diff(y(x),x)+x*y(x)=a*x,y(0) = 2*a],y(x), singsol=all)
\[ y \relax (x ) = -i \sqrt {x -1}\, \sqrt {x +1}\, a +a \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 21
DSolve[{(1-x^2)*y'[x]+x*y[x]==a*x,y[0]==2*a},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to a-i a \sqrt {x^2-1} \\ \end{align*}