29.10.19 problem 285

Internal problem ID [4885]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 285
Date solved : Monday, January 27, 2025 at 09:46:24 AM
CAS classification : [_linear]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime }+x^{2}+y x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 53

dsolve((-x^2+1)*diff(y(x),x)+x^2+x*y(x) = 0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (x^{2}-1\right ) \ln \left (x +\sqrt {x^{2}-1}\right )-\sqrt {x^{2}-1}\, \left (-\sqrt {x -1}\, \sqrt {x +1}\, c_{1} +x \right )}{\sqrt {x^{2}-1}} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 35

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

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