4.5.27 \((x+1) y'(x)=a y(x)+b x y(x)^2\)

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

\[ \left \{ {\frac {bx}{1+a}}-{\frac {b}{a \left (1+a \right ) }}- \left (1+x \right ) ^{-a}{\it \_C1}+ \left (y \relax (x ) \right ) ^{-1}=0 \right \} \] 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