ODE
\[ y(x) y''(x)+y'(x)^2+y(x)^2=0 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.400749 (sec), leaf count = 25
\[\left \{\left \{y(x)\to c_2 \sqrt {\cos \left (\sqrt {2} (x-c_1)\right )}\right \}\right \}\]
Maple ✓
cpu = 0.696 (sec), leaf count = 61
\[\left [y \left (x \right ) = \sqrt {-\sqrt {2}\, \textit {\_C1} \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right ) \sqrt {2}\, \textit {\_C2}}, y \left (x \right ) = -\sqrt {-\sqrt {2}\, \textit {\_C1} \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right ) \sqrt {2}\, \textit {\_C2}}\right ]\] Mathematica raw input
DSolve[y[x]^2 + y'[x]^2 + y[x]*y''[x] == 0,y[x],x]
Mathematica raw output
{{y[x] -> C[2]*Sqrt[Cos[Sqrt[2]*(x - C[1])]]}}
Maple raw input
dsolve(y(x)*diff(diff(y(x),x),x)+diff(y(x),x)^2+y(x)^2 = 0, y(x))
Maple raw output
[y(x) = (-2^(1/2)*_C1*sin(2^(1/2)*x)+cos(2^(1/2)*x)*2^(1/2)*_C2)^(1/2), y(x) = -(-2^(1/2)*_C1*sin(2^(1/2)*x)+cos(2^(1/2)*x)*2^(1/2)*_C2)^(1/2)]