Internal problem ID [3480]
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]
\[ \boxed {\left (x +1\right ) y^{\prime }-y a -b x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve((1+x)*diff(y(x),x) = a*y(x)+b*x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (a +1\right ) a}{\left (x +1\right )^{-a} c_{1} a^{2}+\left (x +1\right )^{-a} c_{1} a -x b a +b} \]
✓ Solution by Mathematica
Time used: 0.299 (sec). Leaf size: 44
DSolve[(1+x) y'[x]==a y[x]+b x y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {a (a+1) (x+1)^a}{b (x+1)^a (a x-1)-a (a+1) c_1} y(x)\to 0 \end{align*}