ODE
\[ y''(x)^2 \left (a^2-b^2 y(x)^2\right )+y'(x)^2 \left (1-b^2 y'(x)^2\right )+2 b^2 y(x) y'(x)^2 y''(x)=0 \] ODE Classification
[[_2nd_order, _missing_x]]
Book solution method
TO DO
Mathematica ✗
cpu = 600.135 (sec), leaf count = 0 , timed out
$Aborted
Maple ✓
cpu = 3.543 (sec), leaf count = 126
\[ \left \{ x-{ab\arctan \left ( {y \left ( x \right ) \sqrt {{b}^{2}}{\frac {1}{\sqrt {{a}^{2}-{b}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) {\frac {1}{\sqrt {{b}^{2}}}}}-{\it \_C1}=0,x+{ab\arctan \left ( {y \left ( x \right ) \sqrt {{b}^{2}}{\frac {1}{\sqrt {{a}^{2}-{b}^{2} \left ( y \left ( x \right ) \right ) ^{2}}}}} \right ) {\frac {1}{\sqrt {{b}^{2}}}}}-{\it \_C1}=0,{a\ln \left ( {\frac {y \left ( x \right ) }{a}\sqrt {{{\it \_C1}}^{2}{b}^{2}-1}}+{\it \_C1} \right ) {\frac {1}{\sqrt {{{\it \_C1}}^{2}{b}^{2}-1}}}}-x-{\it \_C2}=0,y \left ( x \right ) ={\it \_C1} \right \} \] Mathematica raw input
DSolve[y'[x]^2*(1 - b^2*y'[x]^2) + 2*b^2*y[x]*y'[x]^2*y''[x] + (a^2 - b^2*y[x]^2)*y''[x]^2 == 0,y[x],x]
Mathematica raw output
$Aborted
Maple raw input
dsolve((a^2-b^2*y(x)^2)*diff(diff(y(x),x),x)^2+2*b^2*y(x)*diff(y(x),x)^2*diff(diff(y(x),x),x)+(1-b^2*diff(y(x),x)^2)*diff(y(x),x)^2 = 0, y(x),'implicit')
Maple raw output
x-a*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*y(x)/(a^2-b^2*y(x)^2)^(1/2))-_C1 = 0, x+a*b/(b^2)^(1/2)*arctan((b^2)^(1/2)*y(x)/(a^2-b^2*y(x)^2)^(1/2))-_C1 = 0, y(x) = _C1, ln((_C1^2*b^2-1)^(1/2)/a*y(x)+_C1)/(_C1^2*b^2-1)^(1/2)*a-x-_C2 = 0