Internal problem ID [8705]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 369.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}+y^{2}=a^{2}} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 68
dsolve(diff(y(x),x)^2+y(x)^2-a^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -a y \left (x \right ) = a y \left (x \right ) = -\tan \left (-x +c_{1} \right ) \sqrt {\frac {a^{2}}{\tan \left (-x +c_{1} \right )^{2}+1}} y \left (x \right ) = \tan \left (-x +c_{1} \right ) \sqrt {\frac {a^{2}}{\tan \left (-x +c_{1} \right )^{2}+1}} \end{align*}
✓ Solution by Mathematica
Time used: 3.278 (sec). Leaf size: 111
DSolve[-a^2 + y[x]^2 + y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} y(x)\to \frac {a \tan (x-c_1)}{\sqrt {\sec ^2(x-c_1)}} y(x)\to -\frac {a \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} y(x)\to \frac {a \tan (x+c_1)}{\sqrt {\sec ^2(x+c_1)}} y(x)\to -a y(x)\to a \end{align*}