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 = 0.283944 (sec), leaf count = 41
\[\left \{\left \{y(x)\to \frac {1}{4} \left (c_1-2 \sqrt {x}\right ){}^2\right \},\left \{y(x)\to \frac {1}{4} \left (c_1+2 \sqrt {x}\right ){}^2\right \}\right \}\]
Maple ✓
cpu = 0.018 (sec), leaf count = 29
\[ \left \{ y \left ( x \right ) =0,[x \left ( {\it \_T} \right ) ={\frac {{\it \_C1}}{ \left ( {\it \_T}-1 \right ) ^{2}}},y \left ( {\it \_T} \right ) ={\frac {{\it \_C1}\,{{\it \_T}}^{2}}{ \left ( {\it \_T}-1 \right ) ^{2}}}] \right \} \] 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),'implicit')
Maple raw output
y(x) = 0, [x(_T) = 1/(_T-1)^2*_C1, y(_T) = 1/(_T-1)^2*_C1*_T^2]