Internal problem ID [4215]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 982.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (a^{2}-y^{2}\right ) {y^{\prime }}^{2}-y^{2}=0} \]
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 126
dsolve((a^2-y(x)^2)*diff(y(x),x)^2 = y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = 0 x -\sqrt {a^{2}-y \left (x \right )^{2}}+\frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )}{\sqrt {a^{2}}}-c_{1} = 0 x +\sqrt {a^{2}-y \left (x \right )^{2}}-\frac {a^{2} \ln \left (\frac {2 a^{2}+2 \sqrt {a^{2}}\, \sqrt {a^{2}-y \left (x \right )^{2}}}{y \left (x \right )}\right )}{\sqrt {a^{2}}}-c_{1} = 0 \end{align*}
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 102
DSolve[(a^2-y[x]^2) (y'[x])^2==y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {$\#$1}^2}-a \text {arctanh}\left (\frac {\sqrt {a^2-\text {$\#$1}^2}}{a}\right )\&\right ][-x+c_1] y(x)\to \text {InverseFunction}\left [\sqrt {a^2-\text {$\#$1}^2}-a \text {arctanh}\left (\frac {\sqrt {a^2-\text {$\#$1}^2}}{a}\right )\&\right ][x+c_1] y(x)\to 0 \end{align*}