ODE
\[ x y'(x)^2=y(x) \] ODE Classification
[[_homogeneous, `class A`], _rational, _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.203253 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{4} \left (-2 \sqrt {x}+c_1\right ){}^2\right \},\left \{y(x)\to \frac {1}{4} \left (2 \sqrt {x}+c_1\right ){}^2\right \}\right \}\]
Maple ✓
cpu = 0.071 (sec), leaf count = 39
\[\left [y \left (x \right ) = 0, y \left (x \right ) = \frac {\left (x +\sqrt {x \textit {\_C1}}\right )^{2}}{x}, y \left (x \right ) = \frac {\left (-x +\sqrt {x \textit {\_C1}}\right )^{2}}{x}\right ]\] Mathematica raw input
DSolve[x*y'[x]^2 == y[x],y[x],x]
Mathematica raw output
{{y[x] -> (-2*Sqrt[x] + C[1])^2/4}, {y[x] -> (2*Sqrt[x] + C[1])^2/4}}
Maple raw input
dsolve(x*diff(y(x),x)^2 = y(x), y(x))
Maple raw output
[y(x) = 0, y(x) = 1/x*(x+(x*_C1)^(1/2))^2, y(x) = 1/x*(-x+(x*_C1)^(1/2))^2]