60.1.368 problem 369

Internal problem ID [10382]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 369
Date solved : Monday, January 27, 2025 at 07:38:35 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}+y^{2}-a^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.036 (sec). Leaf size: 60

dsolve(diff(y(x),x)^2+y(x)^2-a^2 = 0,y(x), singsol=all)
 

\begin{align*} y &= -a \\ y &= a \\ y &= -\tan \left (-x +c_{1} \right ) \sqrt {\cos \left (-x +c_{1} \right )^{2} a^{2}} \\ y &= \tan \left (-x +c_{1} \right ) \sqrt {\cos \left (-x +c_{1} \right )^{2} a^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 3.306 (sec). Leaf size: 111

DSolve[-a^2 + y[x]^2 + D[y[x],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*}