69.1.18 problem 21

Internal problem ID [14171]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 21
Date solved : Tuesday, January 28, 2025 at 06:18:40 AM
CAS classification : [_separable]

\begin{align*} \left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 9

dsolve((1+x^2)*diff(y(x),x)-sqrt(1-y(x)^2)=0,y(x), singsol=all)
 

\[ y = \sin \left (\arctan \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.256 (sec). Leaf size: 34

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

\begin{align*} y(x)\to \sin \left (\int _1^x\frac {1}{K[1]^2+1}dK[1]+c_1\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}