80.4.7 problem 7

Internal problem ID [18558]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 31. Problems at page 85
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 11:58:52 AM
CAS classification : [_Bernoulli]

\begin{align*} y-y^{\prime } \cos \left (x \right )&=y^{2} \cos \left (x \right ) \left (1-\sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(y(x)-cos(x)*diff(y(x),x)=y(x)^2*cos(x)*(1-sin(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\cos \left (x \right )+\sin \left (x \right )+1}{\left (c_{1} +\sin \left (x \right )\right ) \left (-\sin \left (x \right )+\cos \left (x \right )+1\right )} \]

✓ Solution by Mathematica

Time used: 0.419 (sec). Leaf size: 41

DSolve[y[x]-Cos[x]*D[y[x],x]==y[x]^2*Cos[x]*(1-Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}}{\cos (x) e^{2 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}+c_1} \\ y(x)\to 0 \\ \end{align*}