4.9.32 \(y(x) y'(x)=\sqrt {a^2+y(x)^2}\)

ODE
\[ y(x) y'(x)=\sqrt {a^2+y(x)^2} \] ODE Classification

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica
cpu = 0.0143621 (sec), leaf count = 43

\[\left \{\left \{y(x)\to -\sqrt {\left (c_1+x\right ){}^2-a^2}\right \},\left \{y(x)\to \sqrt {\left (c_1+x\right ){}^2-a^2}\right \}\right \}\]

Maple
cpu = 0.009 (sec), leaf count = 18

\[ \left \{ x-\sqrt { \left (y \relax (x ) \right ) ^{2}+{a}^{2}}+{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y[x]*y'[x] == Sqrt[a^2 + y[x]^2],y[x],x]

Mathematica raw output

{{y[x] -> -Sqrt[-a^2 + (x + C[1])^2]}, {y[x] -> Sqrt[-a^2 + (x + C[1])^2]}}

Maple raw input

dsolve(y(x)*diff(y(x),x) = (y(x)^2+a^2)^(1/2), y(x),'implicit')

Maple raw output

x-(y(x)^2+a^2)^(1/2)+_C1 = 0