Internal problem ID [3445]
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]
\[ \boxed {x y^{\prime }+y-a \left (x^{2}+1\right ) y^{3}=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (x \right ) = \frac {1}{\sqrt {-2 x^{2} \ln \left (x \right ) a +c_{1} x^{2}+a}} y \left (x \right ) = -\frac {1}{\sqrt {-2 x^{2} \ln \left (x \right ) a +c_{1} x^{2}+a}} \end{align*}
✓ Solution by Mathematica
Time used: 0.545 (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*}