Internal problem ID [3533]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 10
Problem number: 277.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }-y=-x^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve((-x^2+1)*diff(y(x),x) = 1-x^2+y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (\sqrt {-\left (x +1\right )^{2}+2 x +2}+\arcsin \left (x \right )+c_{1} \right ) \left (x +1\right )}{\sqrt {-x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 56
DSolve[(1-x^2)y'[x]==1-x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\sqrt {x+1} \left (-2 \arctan \left (\frac {\sqrt {1-x^2}}{x-1}\right )+\sqrt {1-x^2}+c_1\right )}{\sqrt {1-x}} \]