29.7.10 problem 185

Internal problem ID [4785]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 7
Problem number : 185
Date solved : Monday, January 27, 2025 at 09:37:47 AM
CAS classification : [_Bernoulli]

\begin{align*} x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 15

dsolve(x*diff(y(x),x)+(1-a*y(x)*ln(x))*y(x) = 0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.166 (sec). Leaf size: 22

DSolve[x D[y[x],x]+(1-a y[x] Log[x])y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{a \log (x)+a+c_1 x} \\ y(x)\to 0 \\ \end{align*}