Internal problem ID [11225]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IV, differential equations of the first order and higher degree than the first.
Article 28. Summary. Page 59
Problem number: Ex 1.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{2} \left ({y^{\prime }}^{2}+1\right )=a^{2}} \]
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 54
dsolve(y(x)^2*(1+diff(y(x),x)^2)=a^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -a \\ y \left (x \right ) &= a \\ y \left (x \right ) &= \sqrt {a^{2}-c_{1}^{2}+2 c_{1} x -x^{2}} \\ y \left (x \right ) &= -\sqrt {\left (a +x -c_{1} \right ) \left (c_{1} +a -x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.344 (sec). Leaf size: 101
DSolve[y[x]^2*(1+(y'[x])^2)==a^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {a^2-(x+c_1){}^2} \\ y(x)\to \sqrt {a^2-(x+c_1){}^2} \\ y(x)\to -\sqrt {a^2-(x-c_1){}^2} \\ y(x)\to \sqrt {a^2-(x-c_1){}^2} \\ y(x)\to -a \\ y(x)\to a \\ \end{align*}