Internal problem ID [3441]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 7
Problem number: 185.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {x y^{\prime }+\left (1-a y \ln \left (x \right )\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (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: 0.154 (sec). Leaf size: 22
DSolve[x y'[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*}