ODE
\[ 2 y(x) y''(x)=3 y'(x)^2 \] ODE Classification
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Book solution method
TO DO
Mathematica ✓
cpu = 0.281812 (sec), leaf count = 16
\[\left \{\left \{y(x)\to \frac {c_2}{(x+2 c_1){}^2}\right \}\right \}\]
Maple ✓
cpu = 0.926 (sec), leaf count = 13
\[\left [y \left (x \right ) = \frac {4}{\left (\textit {\_C1} x +\textit {\_C2} \right )^{2}}\right ]\] Mathematica raw input
DSolve[2*y[x]*y''[x] == 3*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2]/(x + 2*C[1])^2}}
Maple raw input
dsolve(2*y(x)*diff(diff(y(x),x),x) = 3*diff(y(x),x)^2, y(x))
Maple raw output
[y(x) = 4/(_C1*x+_C2)^2]