29.10.13 problem 279

Internal problem ID [4879]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 279
Date solved : Monday, January 27, 2025 at 09:46:13 AM
CAS classification : [_linear]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }&=5-y x \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve((-x^2+1)*diff(y(x),x) = 5-x*y(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \sqrt {x -1}\, \sqrt {x +1}\, c_{1} +5 x \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 21

DSolve[(1-x^2)D[y[x],x]==5 -x y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 x+c_1 \sqrt {x^2-1} \]