29.25.33 problem 730

Internal problem ID [5320]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 25
Problem number : 730
Date solved : Tuesday, January 28, 2025 at 02:41:51 PM
CAS classification : [`y=_G(x,y')`]

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

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 27

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

\[ y \left (x \right )-\arctan \left (\frac {y \left (x \right )}{\sqrt {x^{2}-y \left (x \right )^{2}}}\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.471 (sec). Leaf size: 29

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

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