35.2.3 problem 3

Internal problem ID [6095]
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
Date solved : Monday, January 27, 2025 at 01:35:46 PM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (\frac {\pi }{3}\right )&={\mathrm e} \end{align*}

✓ Solution by Maple

Time used: 0.208 (sec). Leaf size: 17

dsolve([diff(y(x),x)*sin(x)=y(x)*ln(y(x)),y(1/3*Pi) = exp(1)],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\left (\cot \left (x \right )-\csc \left (x \right )\right ) \sqrt {3}} \]

✓ Solution by Mathematica

Time used: 0.226 (sec). Leaf size: 19

DSolve[{D[y[x],x]*Sin[x]==y[x]*Log[y[x]],{y[Pi/3]==Exp[1]}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{e^{\text {arctanh}\left (\frac {1}{2}\right )-\text {arctanh}(\cos (x))}} \]