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