29.12.12 problem 331

Internal problem ID [4931]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 12
Problem number : 331
Date solved : Monday, January 27, 2025 at 09:52:31 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 25

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

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

✓ Solution by Mathematica

Time used: 0.182 (sec). Leaf size: 40

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

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