Internal problem ID [5275]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary
problems. Page 33
Problem number: 24 (g).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {-\sqrt {a^{2}-x^{2}}\, y^{\prime }=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
dsolve(1-(sqrt(a^2-x^2))*diff(y(x),x)=0,y(x), singsol=all)
\[ y = \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 24
DSolve[1-(Sqrt[a^2-x^2])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \arctan \left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \]