Internal problem ID [3831]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 581.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {3 y^{\prime } x^{2} y+2 y^{2} x=-1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(3*x^2*y(x)*diff(y(x),x)+1+2*x*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {x^{\frac {10}{3}} \left (-2 x^{\frac {1}{3}}+c_{1} \right )}}{x^{\frac {7}{3}}} \\ y \left (x \right ) &= -\frac {\sqrt {x^{\frac {10}{3}} \left (-2 x^{\frac {1}{3}}+c_{1} \right )}}{x^{\frac {7}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.776 (sec). Leaf size: 47
DSolve[3 x^2 y[x] y'[x]+1+2 x y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {2}{x}+\frac {c_1}{x^{4/3}}} \\ y(x)\to \sqrt {-\frac {2}{x}+\frac {c_1}{x^{4/3}}} \\ \end{align*}