Internal problem ID [2032]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 11, page 45
Problem number: 22.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime }+y x -x \left (-x^{2}+1\right ) \sqrt {y}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.343 (sec). Leaf size: 46
dsolve([(1-x^2)*diff(y(x),x)+x*y(x)=x*(1-x^2)*sqrt(y(x)),y(0) = 1],y(x), singsol=all)
\[ y = \left (\frac {4}{9}-\frac {4 i}{9}\right ) \left (x -1\right )^{\frac {5}{4}} \left (x +1\right )^{\frac {5}{4}} \sqrt {2}+\frac {x^{4}}{9}-\frac {16 i \sqrt {x -1}\, \sqrt {x +1}}{9}-\frac {2 x^{2}}{9}+\frac {1}{9} \]
✓ Solution by Mathematica
Time used: 0.228 (sec). Leaf size: 130
DSolve[{(1-x^2)*y'[x]+x*y[x]==x*(1-x^2)*Sqrt[y[x]],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} \left (x^4+\left (4 (-1)^{3/4} \sqrt [4]{x^2-1}-2\right ) x^2-4 i \sqrt {x^2-1}-4 (-1)^{3/4} \sqrt [4]{x^2-1}+1\right ) y(x)\to \frac {1}{9} \left (x^4-2 \left (4 (-1)^{3/4} \sqrt [4]{x^2-1}+1\right ) x^2-16 i \sqrt {x^2-1}+8 (-1)^{3/4} \sqrt [4]{x^2-1}+1\right ) \end{align*}