Internal problem ID [2186]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page
79
Problem number: Problem 47.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {y^{\prime }-\frac {y}{2 x \ln \left (x \right )}-2 x y^{3}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 90
dsolve(diff(y(x),x)-1/(2*x*ln(x))*y(x)=2*x*y(x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {\sqrt {-\left (2 \ln \left (x \right ) x^{2}-x^{2}-c_{1} \right ) \ln \left (x \right )}}{2 \ln \left (x \right ) x^{2}-x^{2}-c_{1}} \\ y \left (x \right ) = -\frac {\sqrt {-\left (2 \ln \left (x \right ) x^{2}-x^{2}-c_{1} \right ) \ln \left (x \right )}}{2 \ln \left (x \right ) x^{2}-x^{2}-c_{1}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.249 (sec). Leaf size: 63
DSolve[y'[x]-1/(2*x*Log[x])*y[x]==2*x*y[x]^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\log (x)}}{\sqrt {x^2-2 x^2 \log (x)+c_1}} \\ y(x)\to \frac {\sqrt {\log (x)}}{\sqrt {x^2-2 x^2 \log (x)+c_1}} \\ y(x)\to 0 \\ \end{align*}