ODE
\[ x y'(x)^2=a \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.163937 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -2 \sqrt {a} \sqrt {x}+c_1\right \},\left \{y(x)\to 2 \sqrt {a} \sqrt {x}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.07 (sec), leaf count = 25
\[\left [y \left (x \right ) = 2 \sqrt {a x}+\textit {\_C1}, y \left (x \right ) = -2 \sqrt {a x}+\textit {\_C1}\right ]\] Mathematica raw input
DSolve[x*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*diff(y(x),x)^2 = a, y(x))
Maple raw output
[y(x) = 2*(a*x)^(1/2)+_C1, y(x) = -2*(a*x)^(1/2)+_C1]