69.1.51 problem 70

Internal problem ID [14204]
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
Date solved : Tuesday, January 28, 2025 at 06:21:46 AM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }&=\left (y \ln \left (x \right )-2\right ) y \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(x*diff(y(x),x)=(y(x)*ln(x)-2)*y(x),y(x), singsol=all)
 

\[ y = \frac {4}{1+4 c_{1} x^{2}+2 \ln \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.155 (sec). Leaf size: 27

DSolve[x*D[y[x],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*}