Internal problem ID [3115]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 13
Problem number: 367.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Bernoulli]
Solve \begin {gather*} \boxed {6 y^{\prime } x^{3}-4 x^{2} y-\left (-3 x +1\right ) y^{4}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 174
dsolve(6*x^3*diff(y(x),x) = 4*x^2*y(x)+(1-3*x)*y(x)^4,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-2 x^{2} \left (-3 x +\ln \relax (x )-2 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{-3 x +\ln \relax (x )-2 c_{1}} \\ y \relax (x ) = -\frac {\left (-2 x^{2} \left (-3 x +\ln \relax (x )-2 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-3 x +\ln \relax (x )-2 c_{1}\right )}-\frac {i \sqrt {3}\, \left (-2 x^{2} \left (-3 x +\ln \relax (x )-2 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-3 x +\ln \relax (x )-2 c_{1}\right )} \\ y \relax (x ) = -\frac {\left (-2 x^{2} \left (-3 x +\ln \relax (x )-2 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (-3 x +\ln \relax (x )-2 c_{1}\right )}+\frac {i \sqrt {3}\, \left (-2 x^{2} \left (-3 x +\ln \relax (x )-2 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{-6 x +2 \ln \relax (x )-4 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.185 (sec). Leaf size: 99
DSolve[6 x^3 y'[x]==4 x^2 y[x]+(1-3 x)y[x]^4,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt [3]{-2} x^{2/3}}{\sqrt [3]{3 x-\log (x)+2 c_1}} \\ y(x)\to \frac {x^{2/3}}{\sqrt [3]{\frac {3 x}{2}-\frac {\log (x)}{2}+c_1}} \\ y(x)\to \frac {(-1)^{2/3} x^{2/3}}{\sqrt [3]{\frac {3 x}{2}-\frac {\log (x)}{2}+c_1}} \\ y(x)\to 0 \\ \end{align*}