Internal problem ID [4154]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 918.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (a^{2}-x^{2}\right ) {y^{\prime }}^{2}=b^{2}} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 44
dsolve((a^2-x^2)*diff(y(x),x)^2 = b^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} y \left (x \right ) = -b \arctan \left (\frac {x}{\sqrt {a^{2}-x^{2}}}\right )+c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 52
DSolve[(a^2-x^2) (y'[x])^2==b^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -b \arctan \left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 y(x)\to b \arctan \left (\frac {x}{\sqrt {a^2-x^2}}\right )+c_1 \end{align*}