81.3.15 problem 15

Internal problem ID [18633]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 15
Date solved : Tuesday, January 28, 2025 at 12:04:57 PM
CAS classification : [_separable]

\begin{align*} \left ({\mathrm e}^{y}+1\right ) \cos \left (x \right )+{\mathrm e}^{y} \sin \left (x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.070 (sec). Leaf size: 24

dsolve((exp(y(x))+1)*cos(x)+exp(y(x))*sin(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = -\ln \left (-\frac {\sin \left (x \right )}{-1+\sin \left (x \right ) {\mathrm e}^{c_{1}}}\right )-c_{1} \]

✓ Solution by Mathematica

Time used: 2.062 (sec). Leaf size: 24

DSolve[(Exp[y[x]]+1)*Cos[x]+Exp[y[x]]*Sin[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \log \left (-1+e^{c_1} \csc (x)\right ) \\ y(x)\to i \pi \\ \end{align*}