Internal problem ID [893]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x +\left (1+\frac {1}{\ln \relax (x )}\right ) y=0} \end {gather*} With initial conditions \begin {align*} [y \left ({\mathrm e}\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.009 (sec). Leaf size: 14
dsolve([x*diff(y(x),x) + (1+1/ln(x))*y(x)=0,y(exp(1)) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}}{x \ln \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 18
DSolve[{y'[x] +(1+1/Log[x])*y[x]==0,y[Exp[1]]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\text {li}(x)+\text {li}(e)-x+e} \\ \end{align*}