4.2.27 \(y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right )\)

ODE
\[ y'(x)=f(x) \left (a+b y(x)+c y(x)^2\right ) \] ODE Classification

[_separable]

Book solution method
Separable ODE, Neither variable missing

Mathematica
cpu = 0.066664 (sec), leaf count = 62

\[\left \{\left \{y(x)\to \frac {\sqrt {4 a c-b^2} \tan \left (\frac {1}{2} \sqrt {4 a c-b^2} \left (\int _1^x f(K[1]) \, dK[1]+c_1\right )\right )-b}{2 c}\right \}\right \}\]

Maple
cpu = 0.011 (sec), leaf count = 44

\[ \left \{ \int \!f \relax (x ) \,{\rm d}x-2\,{\frac {1}{\sqrt {4\,ca-{b}^{2}}}\arctan \left ({\frac {2\,cy \relax (x ) +b}{\sqrt {4\,ca-{b}^{2}}}} \right ) }+{\it \_C1}=0 \right \} \] Mathematica raw input

DSolve[y'[x] == f[x]*(a + b*y[x] + c*y[x]^2),y[x],x]

Mathematica raw output

{{y[x] -> (-b + Sqrt[-b^2 + 4*a*c]*Tan[(Sqrt[-b^2 + 4*a*c]*(C[1] + Integrate[f[K
[1]], {K[1], 1, x}]))/2])/(2*c)}}

Maple raw input

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

Maple raw output

Int(f(x),x)-2/(4*a*c-b^2)^(1/2)*arctan((2*c*y(x)+b)/(4*a*c-b^2)^(1/2))+_C1 = 0