ODE
\[ x^3 y'(x)^2=a \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.154845 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\frac {2 \sqrt {a}}{\sqrt {x}}+c_1\right \},\left \{y(x)\to \frac {2 \sqrt {a}}{\sqrt {x}}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.069 (sec), leaf count = 31
\[\left [y \left (x \right ) = -\frac {2 \sqrt {a x}}{x}+\textit {\_C1}, y \left (x \right ) = \frac {2 \sqrt {a x}}{x}+\textit {\_C1}\right ]\] 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))
Maple raw output
[y(x) = -2/x*(a*x)^(1/2)+_C1, y(x) = 2/x*(a*x)^(1/2)+_C1]