Internal problem ID [12417]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 2. The Initial Value Problem. Exercises 2.4.4, page 115
Problem number: 13 (c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-x \sqrt {-y^{2}+1}=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = {\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve([diff(y(x),x)=x*sqrt(1-y(x)^2),y(0) = 1/2],y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\frac {x^{2}}{2}+\frac {\pi }{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 33
DSolve[{y'[x]==x*Sqrt[1-y[x]^2],{y[0]==1/2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sin \left (\frac {1}{6} \left (\pi -3 x^2\right )\right ) y(x)\to \sin \left (\frac {1}{6} \left (3 x^2+\pi \right )\right ) \end{align*}