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 = 0.0307311 (sec), leaf count = 20
\[\left \{\left \{y(x)\to \frac {c_2}{\left (3 c_1+2 x\right ){}^{3/2}}\right \}\right \}\]
Maple ✓
cpu = 0.016 (sec), leaf count = 17
\[ \left \{ -{\frac {3}{2} \left ( y \left ( x \right ) \right ) ^{-{\frac {2}{3}}}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] 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),'implicit')
Maple raw output
-3/2/y(x)^(2/3)-_C1*x-_C2 = 0