Internal problem ID [12148]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 70.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {x y^{\prime }-\left (y \ln \left (x \right )-2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(x*diff(y(x),x)=(y(x)*ln(x)-2)*y(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {4}{1+4 c_{1} x^{2}+2 \ln \left (x \right )} \]
✓ Solution by Mathematica
Time used: 0.254 (sec). Leaf size: 27
DSolve[x*y'[x]==(y[x]*Log[x]-2)*y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {4}{4 c_1 x^2+2 \log (x)+1} y(x)\to 0 \end{align*}