ODE
\[ (x+1) y'(x)=a y(x)+b x y(x)^2 \] ODE Classification
[_rational, _Bernoulli]
Book solution method
The Bernoulli ODE
Mathematica ✓
cpu = 0.0265106 (sec), leaf count = 39
\[\left \{\left \{y(x)\to -\frac {a (a+1) (x+1)^a}{b (x+1)^a (a x-1)-a (a+1) c_1}\right \}\right \}\]
Maple ✓
cpu = 0.01 (sec), leaf count = 37
\[ \left \{ {\frac {bx}{1+a}}-{\frac {b}{a \left ( 1+a \right ) }}- \left ( 1+x \right ) ^{-a}{\it \_C1}+ \left ( y \left ( x \right ) \right ) ^{-1}=0 \right \} \] Mathematica raw input
DSolve[(1 + x)*y'[x] == a*y[x] + b*x*y[x]^2,y[x],x]
Mathematica raw output
{{y[x] -> -((a*(1 + a)*(1 + x)^a)/(b*(1 + x)^a*(-1 + a*x) - a*(1 + a)*C[1]))}}
Maple raw input
dsolve((1+x)*diff(y(x),x) = a*y(x)+b*x*y(x)^2, y(x),'implicit')
Maple raw output
1/(1+a)*b*x-1/a/(1+a)*b-(1+x)^(-a)*_C1+1/y(x) = 0