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

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

[_quadrature]

Book solution method
Separable ODE, Independent variable missing

Mathematica
cpu = 0.264782 (sec), leaf count = 54

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

Maple
cpu = 0.045 (sec), leaf count = 57

$\left [y \left (x \right ) = -\frac {-\tan \left (\frac {\textit {\_C1} \sqrt {4 \mathit {a0} \mathit {a2} -\mathit {a1}^{2}}}{2}+\frac {x \sqrt {4 \mathit {a0} \mathit {a2} -\mathit {a1}^{2}}}{2}\right ) \sqrt {4 \mathit {a0} \mathit {a2} -\mathit {a1}^{2}}+\mathit {a1}}{2 \mathit {a2}}\right ]$ 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))

Maple raw output

[y(x) = -1/2*(-tan(1/2*_C1*(4*a0*a2-a1^2)^(1/2)+1/2*x*(4*a0*a2-a1^2)^(1/2))*(4*a
0*a2-a1^2)^(1/2)+a1)/a2]