ODE
\[ x^3 y'(x)^2=a \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.00572455 (sec), leaf count = 39
\[\left \{\left \{y(x)\to c_1-\frac {2 \sqrt {a}}{\sqrt {x}}\right \},\left \{y(x)\to \frac {2 \sqrt {a}}{\sqrt {x}}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.025 (sec), leaf count = 31
\[ \left \{ y \left ( x \right ) =-2\,{\frac {\sqrt {ax}}{x}}+{\it \_C1},y \left ( x \right ) =2\,{\frac {\sqrt {ax}}{x}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[x^3*y'[x]^2 == a,y[x],x]
Mathematica raw output
{{y[x] -> (-2*Sqrt[a])/Sqrt[x] + C[1]}, {y[x] -> (2*Sqrt[a])/Sqrt[x] + C[1]}}
Maple raw input
dsolve(x^3*diff(y(x),x)^2 = a, y(x),'implicit')
Maple raw output
y(x) = -2/x*(a*x)^(1/2)+_C1, y(x) = 2/x*(a*x)^(1/2)+_C1