29.14.9 problem 390

Internal problem ID [4988]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 390
Date solved : Monday, January 27, 2025 at 10:01:23 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } \sqrt {-x^{2}+1}&=1+y^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 9

dsolve(diff(y(x),x)*sqrt(-x^2+1) = 1+y(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = \tan \left (\arcsin \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.328 (sec). Leaf size: 25

DSolve[D[y[x],x] Sqrt[1-x^2]==1+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \tan (\arcsin (x)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}