Internal problem ID [3623]
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]
\[ \boxed {6 y^{\prime } x^{3}-4 x^{2} y-\left (1-3 x \right ) y^{4}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 129
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 \left (x \right ) &= \frac {2^{\frac {1}{3}} \left (-x^{2} \left (-3 x +\ln \left (x \right )-2 c_{1} \right )^{2}\right )^{\frac {1}{3}}}{-3 x +\ln \left (x \right )-2 c_{1}} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \left (-x^{2} \left (-3 x +\ln \left (x \right )-2 c_{1} \right )^{2}\right )^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{6 x -2 \ln \left (x \right )+4 c_{1}} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \left (-x^{2} \left (-3 x +\ln \left (x \right )-2 c_{1} \right )^{2}\right )^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{-6 x +2 \ln \left (x \right )-4 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.21 (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*}