ODE
\[ 3 y(x) y''(x)=2 y'(x)^2+36 y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.304432 (sec), leaf count = 27
\[\left \{\left \{y(x)\to c_2 e^{-6 x} \left (e^{4 x}+e^{12 c_1}\right ){}^3\right \}\right \}\]
Maple ✓
cpu = 1.143 (sec), leaf count = 24
\[\left [y \left (x \right ) = \frac {\left ({\mathrm e}^{-4 x} \textit {\_C1} -\textit {\_C2} \right )^{3} {\mathrm e}^{6 x}}{1728}\right ]\] Mathematica raw input
DSolve[3*y[x]*y''[x] == 36*y[x]^2 + 2*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> ((E^(4*x) + E^(12*C[1]))^3*C[2])/E^(6*x)}}
Maple raw input
dsolve(3*y(x)*diff(diff(y(x),x),x) = 2*diff(y(x),x)^2+36*y(x)^2, y(x))
Maple raw output
[y(x) = 1/1728*(exp(-4*x)*_C1-_C2)^3/exp(-2*x)^3]