ODE
\[ y'(x)=\sqrt {a+b y(x)^2} \] ODE Classification
[_quadrature]
Book solution method
Separable ODE, Independent variable missing
Mathematica ✓
cpu = 0.301869 (sec), leaf count = 82
\[\left \{\left \{y(x)\to -\frac {\sqrt {a} \tanh \left (\sqrt {b} (x+c_1)\right )}{\sqrt {b \text {sech}^2\left (\sqrt {b} (x+c_1)\right )}}\right \},\left \{y(x)\to \frac {\sqrt {a} \tanh \left (\sqrt {b} (x+c_1)\right )}{\sqrt {b \text {sech}^2\left (\sqrt {b} (x+c_1)\right )}}\right \}\right \}\]
Maple ✓
cpu = 0.011 (sec), leaf count = 29
\[\left [x -\frac {\ln \left (y \left (x \right ) \sqrt {b}+\sqrt {a +b y \left (x \right )^{2}}\right )}{\sqrt {b}}+\textit {\_C1} = 0\right ]\] Mathematica raw input
DSolve[y'[x] == Sqrt[a + b*y[x]^2],y[x],x]
Mathematica raw output
{{y[x] -> -((Sqrt[a]*Tanh[Sqrt[b]*(x + C[1])])/Sqrt[b*Sech[Sqrt[b]*(x + C[1])]^2])}, {y[x] -> (Sqrt[a]*Tanh[Sqrt[b]*(x + C[1])])/Sqrt[b*Sech[Sqrt[b]*(x + C[1])]^2]}}
Maple raw input
dsolve(diff(y(x),x) = (a+b*y(x)^2)^(1/2), y(x))
Maple raw output
[x-ln(y(x)*b^(1/2)+(a+b*y(x)^2)^(1/2))/b^(1/2)+_C1 = 0]