4.9.27 \(y(x) y'(x)=a x+b y(x)^2\)

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

[_rational, _Bernoulli]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0132547 (sec), leaf count = 77

\[\left \{\left \{y(x)\to -\frac {i \sqrt {a \left (b x+\frac {1}{2}\right )-b^2 c_1 e^{2 b x}}}{b}\right \},\left \{y(x)\to \frac {i \sqrt {a \left (b x+\frac {1}{2}\right )-b^2 c_1 e^{2 b x}}}{b}\right \}\right \}\]

Maple
cpu = 0.008 (sec), leaf count = 28

\[ \left \{ \left (y \relax (x ) \right ) ^{2}+{\frac {ax}{b}}+{\frac {a}{2\,{b}^{2}}}-{{\rm e}^{2\,bx}}{\it \_C1}=0 \right \} \] Mathematica raw input

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

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