19.1.13 problem 13

Internal problem ID [3527]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 13
Date solved : Monday, January 27, 2025 at 07:40:38 AM
CAS classification : [_separable]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+y x&=a x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 a \end{align*}

✓ Solution by Maple

Time used: 0.013 (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)
 

\[ y \left (x \right ) = a \left (1-i \sqrt {x -1}\, \sqrt {x +1}\right ) \]

✓ Solution by Mathematica

Time used: 0.044 (sec). Leaf size: 21

DSolve[{(1-x^2)*D[y[x],x]+x*y[x]==a*x,y[0]==2*a},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to a-i a \sqrt {x^2-1} \]