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

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

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica
cpu = 0.0555641 (sec), leaf count = 43

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

Maple
cpu = 0.01 (sec), leaf count = 29

\[ \left \{ x-{1\ln \left (\sqrt {b}y \relax (x ) +\sqrt {a+b \left (y \relax (x ) \right ) ^{2}} \right ) {\frac {1}{\sqrt {b}}}}+{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

{{y[x] -> (-(a*b) + E^(2*Sqrt[b]*(x + C[1])))/(2*b*E^(Sqrt[b]*(x + C[1])))}}

Maple raw input

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

Maple raw output

x-ln(b^(1/2)*y(x)+(a+b*y(x)^2)^(1/2))/b^(1/2)+_C1 = 0