Internal problem ID [4032]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.19, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [NONE]
Solve \begin {gather*} \boxed {\left (x y \sqrt {x^{2}-y^{2}}+x \right ) y^{\prime }-y+x^{2} \sqrt {x^{2}-y^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 34
dsolve((x*y(x)*sqrt(x^2-y(x)^2)+x)*diff(y(x),x)=y(x)-x^2*sqrt(x^2-y(x)^2),y(x), singsol=all)
\[ \frac {y \relax (x )^{2}}{2}+\arctan \left (\frac {y \relax (x )}{\sqrt {x^{2}-y \relax (x )^{2}}}\right )+\frac {x^{2}}{2}-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 2.854 (sec). Leaf size: 44
DSolve[(x*y[x]*Sqrt[x^2-y[x]^2]+x)*y'[x]==y[x]-x^2*Sqrt[x^2-y[x]^2],y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\text {ArcTan}\left (\frac {\sqrt {x^2-y(x)^2}}{y(x)}\right )+\frac {x^2}{2}+\frac {y(x)^2}{2}=c_1,y(x)\right ] \]