Internal problem ID [3645]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 31
Problem number: 917.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {\left (a^{2}-x^{2}\right ) \left (y^{\prime }\right )^{2}+b^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.104 (sec). Leaf size: 44
dsolve((a^2-x^2)*diff(y(x),x)^2+b^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = b \ln \left (x +\sqrt {-a^{2}+x^{2}}\right )+c_{1} \\ y \relax (x ) = -b \ln \left (x +\sqrt {-a^{2}+x^{2}}\right )+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.009 (sec). Leaf size: 52
DSolve[(a^2-x^2) (y'[x])^2+b^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -b \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-a^2}}\right )+c_1 \\ y(x)\to b \tanh ^{-1}\left (\frac {x}{\sqrt {x^2-a^2}}\right )+c_1 \\ \end{align*}