Internal problem ID [4243]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 2. Separable equations. page
398
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \sin \relax (x )-y \ln \relax (y)=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{3}\right ) = {\mathrm e}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.287 (sec). Leaf size: 18
dsolve([diff(y(x),x)*sin(x)=y(x)*ln(y(x)),y(1/3*Pi) = exp(1)],y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{-\frac {\sqrt {3}\, \left (\cos \relax (x )-1\right )}{\sin \relax (x )}} \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 19
DSolve[{y'[x]*Sin[x]==y[x]*Log[y[x]],{y[Pi/3]==Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\sqrt {3} \tan \left (\frac {x}{2}\right )} \\ \end{align*}