40.3.14 problem 24 (g)

Internal problem ID [6618]
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)
Date solved : Monday, January 27, 2025 at 02:16:09 PM
CAS classification : [_quadrature]

\begin{align*} 1-\sqrt {a^{2}-x^{2}}\, y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (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])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \arctan \left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \]