4.2.10 $y^{\prime }(x)=\text{a0}+\text{a1}y(x)+\text{a2}y(x{)}^2$

ODE
$$y^{\prime }(x)=\text{a0}+\text{a1}y(x)+\text{a2}y(x{)}^2$$ ODE Classification

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica ✓
cpu = 0.0369065 (sec), leaf count = 54

$$\left\{\{y(x)\to \frac{\sqrt{4\text{a0}\text{a2}-{\text{a1}}^2}\tan \left(\frac{1}{2}(c_1+x)\sqrt{4\text{a0}\text{a2}-{\text{a1}}^2}\right)-\text{a1}}{2\text{a2}}\}\right\}$$

Maple ✓
cpu = 0.012 (sec), leaf count = 41

$$\{x-2\frac{1}{\sqrt{4\mathit{a}\mathit{0}\mathit{a}\mathit{2}-{\mathit{a}\mathit{1}}^2}}\arctan \left(\frac{2\mathit{a}\mathit{2}y\left(x\right)+\mathit{a}\mathit{1}}{\sqrt{4\mathit{a}\mathit{0}\mathit{a}\mathit{2}-{\mathit{a}\mathit{1}}^2}}\right)+\mathit{\_}\mathit{C}\mathit{1}=0\}$$ Mathematica raw input

DSolve[y'[x] == a0 + a1*y[x] + a2*y[x]^2,y[x],x]

Mathematica raw output

{{y[x] -> (-a1 + Sqrt[-a1^2 + 4*a0*a2]*Tan[(Sqrt[-a1^2 + 4*a0*a2]*(x + C[1]))/2]
)/(2*a2)}}

Maple raw input

dsolve(diff(y(x),x) = a0+a1*y(x)+a2*y(x)^2, y(x),'implicit')

Maple raw output

x-2/(4*a0*a2-a1^2)^(1/2)*arctan((2*a2*y(x)+a1)/(4*a0*a2-a1^2)^(1/2))+_C1 = 0