Internal problem ID [8827]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 492.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {\left (y^{2}-a^{2}\right ) {y^{\prime }}^{2}+y^{2}=0} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 115
dsolve((y(x)^2-a^2)*diff(y(x),x)^2+y(x)^2 = 0,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 {-y \left (x \right )^{2}+a^{2}}+a \right )}{y \left (x \right )}\right )-\sqrt {-y \left (x \right )^{2}+a^{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 {-y \left (x \right )^{2}+a^{2}}+a \right )}{y \left (x \right )}\right )+\sqrt {-y \left (x \right )^{2}+a^{2}}-c_{1} +x &= 0 \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.317 (sec). Leaf size: 102
DSolve[y[x]^2 + (-a^2 + y[x]^2)*y'[x]^2==0,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*}