Internal problem ID [498]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {-x^{2}+1}\, y^{2} y^{\prime }-\arcsin \relax (x )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.129 (sec). Leaf size: 16
dsolve([(-x^2+1)^(1/2)*y(x)^2*diff(y(x),x) = arcsin(x),y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (8+12 \arcsin \relax (x )^{2}\right )^{\frac {1}{3}}}{2} \]
✓ Solution by Mathematica
Time used: 0.474 (sec). Leaf size: 19
DSolve[{(-x^2+1)^(1/2)*y[x]^2*y'[x] == ArcSin[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt [3]{\frac {3 \text {ArcSin}(x)^2}{2}+1} \\ \end{align*}