ODE
\[ y(x) y''(x)+y'(x)^2=a^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.374225 (sec), leaf count = 64
\[\left \{\left \{y(x)\to -\frac {\sqrt {a^4 (x+c_2){}^2-e^{2 c_1}}}{a}\right \},\left \{y(x)\to \frac {\sqrt {a^4 (x+c_2){}^2-e^{2 c_1}}}{a}\right \}\right \}\]
Maple ✓
cpu = 0.181 (sec), leaf count = 43
\[\left [y \left (x \right ) = \sqrt {a^{2} x^{2}-2 \textit {\_C1} x +2 \textit {\_C2}}, y \left (x \right ) = -\sqrt {a^{2} x^{2}-2 \textit {\_C1} x +2 \textit {\_C2}}\right ]\] Mathematica raw input
DSolve[y'[x]^2 + y[x]*y''[x] == a^2,y[x],x]
Mathematica raw output
{{y[x] -> -(Sqrt[-E^(2*C[1]) + a^4*(x + C[2])^2]/a)}, {y[x] -> Sqrt[-E^(2*C[1]) + a^4*(x + C[2])^2]/a}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+diff(y(x),x)^2 = a^2, y(x))
Maple raw output
[y(x) = (a^2*x^2-2*_C1*x+2*_C2)^(1/2), y(x) = -(a^2*x^2-2*_C1*x+2*_C2)^(1/2)]