Internal problem ID [3323]
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]
Solve \begin {gather*} \boxed {3 y y^{\prime } x^{2}+1+2 x y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 50
dsolve(3*x^2*y(x)*diff(y(x),x)+1+2*x*y(x)^2 = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\sqrt {-x^{\frac {7}{3}} \left (2 x^{\frac {4}{3}}-c_{1} x \right )}}{x^{\frac {7}{3}}} \\ y \relax (x ) = -\frac {\sqrt {-x^{\frac {7}{3}} \left (2 x^{\frac {4}{3}}-c_{1} x \right )}}{x^{\frac {7}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.35 (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*}