Internal problem ID [4370]
Book: Differential Equations, By George Boole F.R.S. 1865
Section: Chapter 2
Problem number: 6.3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+\frac {y}{\left (-x^{2}+1\right )^{\frac {3}{2}}}=\frac {x +\sqrt {-x^{2}+1}}{\left (-x^{2}+1\right )^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(diff(y(x),x)+y(x)/(1-x^2)^(3/2)=(x+sqrt(1-x^2))/(1-x^2)^2,y(x), singsol=all)
\[ y \left (x \right ) = \left (\int \frac {{\mathrm e}^{\frac {x}{\sqrt {-x^{2}+1}}} \left (x +\sqrt {-x^{2}+1}\right )}{\left (x -1\right )^{2} \left (x +1\right )^{2}}d x +c_{1} \right ) {\mathrm e}^{\frac {\left (x -1\right ) \left (x +1\right ) x}{\left (-x^{2}+1\right )^{\frac {3}{2}}}} \]
✓ Solution by Mathematica
Time used: 0.169 (sec). Leaf size: 38
DSolve[y'[x]+y[x]/(1-x^2)^(3/2)==(x+Sqrt[1-x^2])/(1-x^2)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x}{\sqrt {1-x^2}}+c_1 e^{-\frac {x}{\sqrt {1-x^2}}} \]