Internal problem ID [7712]
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]
Solve \begin {gather*} \boxed {3 x y^{\prime }-3 x \ln \relax (x ) y^{4}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 234
dsolve(3*x*diff(y(x),x) - 3*x*ln(x)*y(x)^4 - y(x)=0,y(x), singsol=all)
\begin{align*} y \relax (x ) = \frac {\left (-4 x \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}} \\ y \relax (x ) = -\frac {\left (-4 x \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )}-\frac {i \sqrt {3}\, \left (-4 x \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )} \\ y \relax (x ) = -\frac {\left (-4 x \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{2 \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )}+\frac {i \sqrt {3}\, \left (-4 x \left (6 \ln \relax (x ) x^{2}-3 x^{2}-4 c_{1}\right )^{2}\right )^{\frac {1}{3}}}{12 \ln \relax (x ) x^{2}-6 x^{2}-8 c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.202 (sec). Leaf size: 119
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]{x} \text {Root}\left [\text {$\#$1}^3-4\&,2\right ]}{\sqrt [3]{3 x^2-6 x^2 \log (x)+4 c_1}} \\ y(x)\to 0 \\ \end{align*}