Internal problem ID [2983]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 8
Problem number: 235.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {\left (-x +a \right ) y^{\prime }-y-\left (c x +b \right ) y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 65
dsolve((a-x)*diff(y(x),x) = y(x)+(c*x+b)*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {c_{1} a^{2}-2 a x c_{1}+c_{1} x^{2}+a c -2 c x -b}} \\ y \relax (x ) = -\frac {1}{\sqrt {c_{1} a^{2}-2 a x c_{1}+c_{1} x^{2}+a c -2 c x -b}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.431 (sec). Leaf size: 66
DSolve[(a-x) y'[x]==y[x]+(b+c x)y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {c (a-2 x)+c_1 (a-x)^2-b}} \\ y(x)\to \frac {1}{\sqrt {c (a-2 x)+c_1 (a-x)^2-b}} \\ y(x)\to 0 \\ \end{align*}