Internal problem ID [2938]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 190.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {y^{\prime } x -a y-b \left (x^{2}+1\right ) y^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 184
dsolve(x*diff(y(x),x) = a*y(x)+b*(x^2+1)*y(x)^3,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-\left (a b \,x^{2+2 a}+a b \,x^{2 a}-c_{1} a^{2}+b \,x^{2 a}-c_{1} a \right ) a \,x^{2 a} \left (a +1\right )}}{a b \,x^{2+2 a}+a b \,x^{2 a}-c_{1} a^{2}+b \,x^{2 a}-c_{1} a} \\ y \relax (x ) = -\frac {\sqrt {-\left (a b \,x^{2+2 a}+a b \,x^{2 a}-c_{1} a^{2}+b \,x^{2 a}-c_{1} a \right ) a \,x^{2 a} \left (a +1\right )}}{a b \,x^{2+2 a}+a b \,x^{2 a}-c_{1} a^{2}+b \,x^{2 a}-c_{1} a} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.795 (sec). Leaf size: 108
DSolve[x y'[x]==a y[x]+b(1+x^2)y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {i \sqrt {a} \sqrt {a+1} x^a}{\sqrt {b x^{2 a} \left (a x^2+a+1\right )-a (a+1) c_1}} \\ y(x)\to \frac {i \sqrt {a} \sqrt {a+1} x^a}{\sqrt {b x^{2 a} \left (a x^2+a+1\right )-a (a+1) c_1}} \\ y(x)\to 0 \\ \end{align*}