15.5.9 problem 9

Internal problem ID [2945]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 02:38:54 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: 0.071 (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: 0.530 (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]
 

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