ODE
\[ 3 y(x) y''(x)=5 y'(x)^2 \] 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 = 0.285414 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \frac {c_2}{(2 x+3 c_1){}^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.104 (sec), leaf count = 17
\[\left [-\frac {3}{2 y \left (x \right )^{\frac {2}{3}}}-\textit {\_C1} x -\textit {\_C2} = 0\right ]\] Mathematica raw input
DSolve[3*y[x]*y''[x] == 5*y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> C[2]/(2*x + 3*C[1])^(3/2)}}
Maple raw input
dsolve(3*y(x)*diff(diff(y(x),x),x) = 5*diff(y(x),x)^2, y(x))
Maple raw output
[-3/2/y(x)^(2/3)-_C1*x-_C2 = 0]