Internal problem ID [3405]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 24
Problem number: 666.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational]
Solve \begin {gather*} \boxed {x \left (x y^{2}+1\right ) y^{\prime }-\left (2-3 x y^{2}\right ) y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.039 (sec). Leaf size: 45
dsolve(x*(1+x*y(x)^2)*diff(y(x),x) = (2-3*x*y(x)^2)*y(x),y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {c_{1}+\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ y \relax (x ) = -\frac {-c_{1}+\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.56 (sec). Leaf size: 75
DSolve[x(1+x y[x]^2)y'[x]==(2-3 x y[x]^2)y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {4 x^5+e^{5 c_1}}+e^{\frac {5 c_1}{2}}}{2 x^3} \\ y(x)\to \frac {\sqrt {4 x^5+e^{5 c_1}}-e^{\frac {5 c_1}{2}}}{2 x^3} \\ \end{align*}