Internal problem ID [8468]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 132.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {3 x y^{\prime }-3 x \ln \left (x \right ) y^{4}-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 162
dsolve(3*x*diff(y(x),x) - 3*x*ln(x)*y(x)^4 - y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {2^{\frac {2}{3}} {\left (-x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}}}{6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1}} \\ y \left (x \right ) &= -\frac {2^{\frac {2}{3}} {\left (-x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (1+i \sqrt {3}\right )}{12 x^{2} \ln \left (x \right )-6 x^{2}-8 c_{1}} \\ y \left (x \right ) &= \frac {2^{\frac {2}{3}} {\left (-x \left (6 x^{2} \ln \left (x \right )-3 x^{2}-4 c_{1} \right )^{2}\right )}^{\frac {1}{3}} \left (i \sqrt {3}-1\right )}{12 x^{2} \ln \left (x \right )-6 x^{2}-8 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.215 (sec). Leaf size: 120
DSolve[3*x*y'[x] - 3*x*Log[x]*y[x]^4 - y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {(-2)^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}} \\ y(x)\to \frac {2^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}} \\ y(x)\to -\frac {\sqrt [3]{-1} 2^{2/3} \sqrt [3]{x}}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}} \\ y(x)\to 0 \\ \end{align*}