Internal problem ID [3025]
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]
Solve \begin {gather*} \boxed {\left (1-x^{2}\right ) y^{\prime }-1+x^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve((-x^2+1)*diff(y(x),x) = 1-x^2+y(x),y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (\sqrt {-\left (x +1\right )^{2}+2 x +2}+\arcsin \relax (x )+c_{1}\right ) \left (x +1\right )}{\sqrt {-x^{2}+1}} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 62
DSolve[(1-x^2)y'[x]==1-x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {\sqrt {x+1} \left (\sqrt {1-x^2}+2 i \log \left (\sqrt {1-x}-i \sqrt {x+1}\right )+c_1\right )}{\sqrt {1-x}} \\ \end{align*}