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

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

[_separable]

Book solution method
The Bernoulli ODE

Mathematica
cpu = 0.0156785 (sec), leaf count = 62

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

Maple
cpu = 0.007 (sec), leaf count = 22

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

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

Mathematica raw output

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

Maple raw input

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

Maple raw output

a/b-exp(b*x^2)*_C1+y(x)^2 = 0