ODE
\[ y(x) y'(x)^2=a^2 x \] ODE Classification
[[_homogeneous, `class A`], _dAlembert]
Book solution method
No Missing Variables ODE, Solve for \(y'\)
Mathematica ✓
cpu = 0.0173141 (sec), leaf count = 46
\[\left \{\left \{y(x)\to \left (\frac {3 c_1}{2}-a x^{3/2}\right ){}^{2/3}\right \},\left \{y(x)\to \left (a x^{3/2}+\frac {3 c_1}{2}\right ){}^{2/3}\right \}\right \}\]
Maple ✓
cpu = 0.026 (sec), leaf count = 40
\[ \left \{ [x \left ( {\it \_T} \right ) ={{{\it \_T}}^{2}{\it \_C1} \left ( {{\it \_T}}^{3}-{a}^{2} \right ) ^{-{\frac {2}{3}}}},y \left ( {\it \_T} \right ) ={{a}^{2}{\it \_C1} \left ( {{\it \_T}}^{3}-{a}^{2} \right ) ^{-{\frac {2}{3}}}}] \right \} \] Mathematica raw input
DSolve[y[x]*y'[x]^2 == a^2*x,y[x],x]
Mathematica raw output
{{y[x] -> (-(a*x^(3/2)) + (3*C[1])/2)^(2/3)}, {y[x] -> (a*x^(3/2) + (3*C[1])/2)^(2/3)}}
Maple raw input
dsolve(y(x)*diff(y(x),x)^2 = a^2*x, y(x),'implicit')
Maple raw output
[x(_T) = 1/(_T^3-a^2)^(2/3)*_T^2*_C1, y(_T) = a^2/(_T^3-a^2)^(2/3)*_C1]