Internal problem ID [2069]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 12, page 46
Problem number: 39.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \sqrt {1-y}-\sqrt {1-x^{2}}\, y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 22
dsolve([x*sqrt(1-y(x))-sqrt(1-x^2)*diff(y(x),x)=0,y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{2}}{4}-\frac {\sqrt {-x^{2}+1}}{2}+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.231 (sec). Leaf size: 53
DSolve[{x*Sqrt[1-y[x]]-Sqrt[1-x^2]*y'[x]==0,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} \left (x^2-2 \sqrt {1-x^2}+2\right ) \\ y(x)\to \frac {1}{4} \left (x^2+6 \sqrt {1-x^2}-6\right ) \\ \end{align*}