10.2.20 problem 20

Internal problem ID [1148]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 20
Date solved : Monday, January 27, 2025 at 04:36:32 AM
CAS classification : [_separable]

\begin{align*} \sqrt {-x^{2}+1}\, y^{2} y^{\prime }&=\arcsin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.115 (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)
 

\[ y = \frac {\left (8+12 \arcsin \left (x \right )^{2}\right )^{{1}/{3}}}{2} \]

✓ Solution by Mathematica

Time used: 0.492 (sec). Leaf size: 19

DSolve[{(-x^2+1)^(1/2)*y[x]^2*D[y[x],x] == ArcSin[x],y[0]==1},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sqrt [3]{\frac {3 \arcsin (x)^2}{2}+1} \]