Internal problem ID [10168]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 13.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \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}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 61
dsolve(diff(y(x),x)+y(x)/(1-x^2)^(3/2)= (x+(1-x^2)^(1/2))/(1-x^2)^2,y(x), singsol=all)
\[ y \relax (x ) = \left (\int \frac {{\mathrm e}^{\frac {x}{\sqrt {-x^{2}+1}}} \left (x +\sqrt {-x^{2}+1}\right )}{\left (x -1\right )^{2} \left (1+x \right )^{2}}d x +c_{1}\right ) {\mathrm e}^{\frac {\left (x -1\right ) \left (1+x \right ) x}{\left (-x^{2}+1\right )^{\frac {3}{2}}}} \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 38
DSolve[y'[x]+y[x]/(1-x^2)^(3/2)== (x+(1-x^2)^(1/2))/(1-x^2)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{\sqrt {1-x^2}}+c_1 e^{-\frac {x}{\sqrt {1-x^2}}} \\ \end{align*}