Internal problem ID [3331]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 21
Problem number: 589.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class G], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {3 x^{4} y y^{\prime }-1+2 x^{3} y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 55
dsolve(3*x^4*y(x)*diff(y(x),x) = 1-2*x^3*y(x)^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {\sqrt {-5 x^{\frac {13}{3}} \left (2 x^{\frac {4}{3}}-5 x^{3} c_{1}\right )}}{5 x^{\frac {13}{3}}} \\ y \relax (x ) = \frac {\sqrt {-5 x^{\frac {13}{3}} \left (2 x^{\frac {4}{3}}-5 x^{3} c_{1}\right )}}{5 x^{\frac {13}{3}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 3.618 (sec). Leaf size: 51
DSolve[3 x^4 y[x] y'[x]==1-2 x^3 y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} \\ y(x)\to \sqrt {-\frac {2}{5 x^3}+\frac {c_1}{x^{4/3}}} \\ \end{align*}