2.1833   ODE No. 1833

\[ y''(x)^2 \left (a^2 y(x)^2-b^2\right )+y'(x)^2 \left (a^2 y'(x)^2-1\right )-2 a^2 y(x) y'(x)^2 y''(x)=0 \]

✓ Mathematica : cpu = 3.17879 (sec), leaf count = 1

DSolve[Derivative[1][y][x]^2*(-1 + a^2*Derivative[1][y][x]^2) - 2*a^2*y[x]*Derivative[1][y][x]^2*Derivative[2][y][x] + (-b^2 + a^2*y[x]^2)*Derivative[2][y][x]^2 == 0,y[x],x]
 

\[\{\}\]

✓ Maple : cpu = 2.641 (sec), leaf count = 162

dsolve((a^2*y(x)^2-b^2)*diff(diff(y(x),x),x)^2-2*a^2*y(x)*diff(y(x),x)^2*diff(diff(y(x),x),x)+(a^2*diff(y(x),x)^2-1)*diff(y(x),x)^2=0,y(x))
 

\[y \left (x \right ) = \frac {\tan \left (\frac {\sqrt {a^{2}}\, \left (-x +c_{1} \right )}{a b}\right ) b}{\sqrt {{\tan \left (\frac {\sqrt {a^{2}}\, \left (-x +c_{1} \right )}{a b}\right )}^{2}+1}\, a}\]