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 = 0.263269 (sec), leaf count = 20
\[\left \{\left \{y(x)\to c_2 (4 x-5 c_1){}^{5/4}\right \}\right \}\]
Maple ✓
cpu = 0.087 (sec), leaf count = 17
\[\left [\frac {5 y \left (x \right )^{\frac {4}{5}}}{4}-\textit {\_C1} x -\textit {\_C2} = 0\right ]\] 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))
Maple raw output
[5/4*y(x)^(4/5)-_C1*x-_C2 = 0]