40.4.12 problem 19 (m)

Internal problem ID [6652]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 6. Equations of first order and first degree (Linear equations). Supplemetary problems. Page 39
Problem number : 19 (m)
Date solved : Tuesday, January 28, 2025 at 03:10:25 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.026 (sec). Leaf size: 27

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

\[ y-\arctan \left (\frac {y}{\sqrt {x^{2}-y^{2}}}\right )-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.492 (sec). Leaf size: 29

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

\[ \text {Solve}\left [\arctan \left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+y(x)=c_1,y(x)\right ] \]