Internal problem ID [2705]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 72.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
Solve \begin {gather*} \boxed {3 y^{\prime } x -3 x y^{4} \ln \relax (x )-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 234
dsolve(3*x*diff(y(x),x)-3*x*y(x)^4*ln(x)-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: 0.242 (sec). Leaf size: 120
DSolve[3*x*y'[x]-3*x*y[x]^4*Log[x]-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*}