ODE
\[ 4 y(x) y''(x)=3 y'(x)^2+12 y(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.362299 (sec), leaf count = 41
\[\left \{\left \{y(x)\to c_2 e^{-2 \sqrt {3} x} \left (e^{\sqrt {3} x}+e^{4 \sqrt {3} c_1}\right ){}^4\right \}\right \}\]
Maple ✓
cpu = 0.689 (sec), leaf count = 29
\[\left [y \left (x \right ) = \frac {\left ({\mathrm e}^{\sqrt {3}\, x} \textit {\_C1} -\textit {\_C2} \right )^{4} {\mathrm e}^{-2 \sqrt {3}\, x}}{2304}\right ]\] Mathematica raw input
DSolve[4*y[x]*y''[x] == 12*y[x]^2 + 3*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> ((E^(Sqrt[3]*x) + E^(4*Sqrt[3]*C[1]))^4*C[2])/E^(2*Sqrt[3]*x)}}
Maple raw input
dsolve(4*y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2+12*y(x)^2, y(x))
Maple raw output
[y(x) = 1/2304*(exp(3^(1/2)*x)*_C1-_C2)^4/exp(1/2*3^(1/2)*x)^4]