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: 0.031 (sec). Leaf size: 115
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 \\ a \,\operatorname {csgn}\left (a \right ) \ln \left (2\right )+a \,\operatorname {csgn}\left (a \right ) \ln \left (\frac {a \left (\operatorname {csgn}\left (a \right ) \sqrt {a^{2}-y \left (x \right )^{2}}+a \right )}{y \left (x \right )}\right )-\sqrt {a^{2}-y \left (x \right )^{2}}-c_{1} +x &= 0 \\ -a \,\operatorname {csgn}\left (a \right ) \ln \left (2\right )-a \,\operatorname {csgn}\left (a \right ) \ln \left (\frac {a \left (\operatorname {csgn}\left (a \right ) \sqrt {a^{2}-y \left (x \right )^{2}}+a \right )}{y \left (x \right )}\right )+\sqrt {a^{2}-y \left (x \right )^{2}}-c_{1} +x &= 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*}