Internal problem ID [7949]
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]
Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+y^{2}-a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.255 (sec). Leaf size: 68
dsolve(diff(y(x),x)^2+y(x)^2-a^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -a \\ y \relax (x ) = a \\ y \relax (x ) = -\tan \left (c_{1}-x \right ) \sqrt {\frac {a^{2}}{\tan ^{2}\left (c_{1}-x \right )+1}} \\ y \relax (x ) = \tan \left (c_{1}-x \right ) \sqrt {\frac {a^{2}}{\tan ^{2}\left (c_{1}-x \right )+1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.178 (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*}