Internal problem ID [14990]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 63.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{2}+2 x \sqrt {a x -x^{2}}\, y^{\prime }=-a^{2}} \] With initial conditions \begin {align*} [y \left (a \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.562 (sec). Leaf size: 22
dsolve([(a^2+y(x)^2)+2*x*sqrt(a*x-x^2)*diff(y(x),x)=0,y(a) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \tan \left (\frac {a -x}{\sqrt {x \left (a -x \right )}}\right ) a \]
✓ Solution by Mathematica
Time used: 31.916 (sec). Leaf size: 23
DSolve[{(a^2+y[x]^2)+2*x*Sqrt[a*x-x^2]*y'[x]==0,{y[a]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to a \tan \left (\frac {\sqrt {x (a-x)}}{x}\right ) \]