ODE
\[ 5 y(x) y''(x)=y'(x)^2 \] 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 = 0.0296704 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 \left (4 x-5 c_1\right ){}^{5/4}\right \}\right \}\]
Maple ✓
cpu = 0.073 (sec), leaf count = 17
\[ \left \{ {\frac {5}{4} \left ( y \left ( x \right ) \right ) ^{{\frac {4}{5}}}}-{\it \_C1}\,x-{\it \_C2}=0 \right \} \] Mathematica raw input
DSolve[5*y[x]*y''[x] == y'[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> (4*x - 5*C[1])^(5/4)*C[2]}}
Maple raw input
dsolve(5*y(x)*diff(diff(y(x),x),x) = diff(y(x),x)^2, y(x),'implicit')
Maple raw output
5/4*y(x)^(4/5)-_C1*x-_C2 = 0