Internal problem ID [3619]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 363.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
\[ \boxed {x \left (-x^{2}+1\right ) y^{\prime }+\left (-x^{2}+1\right ) y^{2}=-x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(x*(-x^2+1)*diff(y(x),x)+x^2+(-x^2+1)*y(x)^2 = 0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\operatorname {EllipticK}\left (x \right )}{c_{1} \operatorname {EllipticCE}\left (x \right )-c_{1} \operatorname {EllipticCK}\left (x \right )+\operatorname {EllipticE}\left (x \right )}+\frac {c_{1} \operatorname {EllipticCE}\left (x \right )+\operatorname {EllipticE}\left (x \right )}{c_{1} \operatorname {EllipticCE}\left (x \right )-c_{1} \operatorname {EllipticCK}\left (x \right )+\operatorname {EllipticE}\left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.971 (sec). Leaf size: 91
DSolve[x(1-x^2)y'[x]+x^2+(1-x^2)y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {2 \left (\pi G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,1 \\ \end {array} \right )+c_1 \left (\operatorname {EllipticK}\left (x^2\right )-\operatorname {EllipticE}\left (x^2\right )\right )\right )}{\pi G_{2,2}^{2,0}\left (x^2| \begin {array}{c} \frac {1}{2},\frac {3}{2} \\ 0,0 \\ \end {array} \right )+2 c_1 \operatorname {EllipticE}\left (x^2\right )} y(x)\to 1-\frac {\operatorname {EllipticK}\left (x^2\right )}{\operatorname {EllipticE}\left (x^2\right )} \end{align*}