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 = 0.328464 (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 = 0.032 (sec), leaf count = 40
\[\left [y \left (x \right ) = \frac {a \left (1+a \right )}{\left (1+x \right )^{-a} \textit {\_C1} \,a^{2}+\left (1+x \right )^{-a} \textit {\_C1} a -a b x +b}\right ]\] 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))
Maple raw output
[y(x) = a*(1+a)/((1+x)^(-a)*_C1*a^2+(1+x)^(-a)*_C1*a-a*b*x+b)]