Internal problem ID [2937]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 189.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x +y-a \left (x^{2}+1\right ) y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 43
dsolve(x*diff(y(x),x)+y(x) = a*(x^2+1)*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {1}{\sqrt {-2 a \ln \relax (x ) x^{2}+c_{1} x^{2}+a}} \\ y \relax (x ) = -\frac {1}{\sqrt {-2 a \ln \relax (x ) x^{2}+c_{1} x^{2}+a}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.338 (sec). Leaf size: 56
DSolve[x y'[x]+y[x]==a(1+x^2)y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{\sqrt {-2 a x^2 \log (x)+a+c_1 x^2}} \\ y(x)\to \frac {1}{\sqrt {-2 a x^2 \log (x)+a+c_1 x^2}} \\ y(x)\to 0 \\ \end{align*}