Internal problem ID [2972]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 224.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (x +1\right ) y^{\prime }-a y-b x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 40
dsolve((1+x)*diff(y(x),x) = a*y(x)+b*x*y(x)^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {a \left (a +1\right )}{\left (x +1\right )^{-a} c_{1} a^{2}+\left (x +1\right )^{-a} c_{1} a -b x a +b} \]
✓ Solution by Mathematica
Time used: 0.304 (sec). Leaf size: 38
DSolve[(1+x) y'[x]==a y[x]+b x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{\frac {b-a b x}{a^2+a}+c_1 (x+1)^{-a}} \\ y(x)\to 0 \\ \end{align*}