29.10.11 problem 277

Internal problem ID [4877]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 10
Problem number : 277
Date solved : Monday, January 27, 2025 at 09:46:09 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 30

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

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

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 56

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

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