Internal problem ID [3913]
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]
\[ \boxed {x \left (1+y^{2} x \right ) y^{\prime }-\left (2-3 y^{2} x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.047 (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 \left (x \right ) = \frac {c_{1} +\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} y \left (x \right ) = -\frac {-c_{1} +\sqrt {4 x^{5}+c_{1}^{2}}}{2 x^{3}} \end{align*}
✓ Solution by Mathematica
Time used: 1.286 (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*}