53.4.14 problem 15

Internal problem ID [8502]
Book : Elementary differential equations. By Earl D. Rainville, Phillip E. Bedient. Macmilliam Publishing Co. NY. 6th edition. 1981.
Section : CHAPTER 16. Nonlinear equations. Section 101. Independent variable missing. EXERCISES Page 324
Problem number : 15
Date solved : Monday, January 27, 2025 at 04:07:32 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)*cos(x)=diff(y(x),x),y(x), singsol=all)
 

\[ y = c_{1} +\left (\ln \left (\sec \left (x \right )+\tan \left (x \right )\right )-\ln \left (\cos \left (x \right )\right )\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.188 (sec). Leaf size: 25

DSolve[D[y[x],{x,2}]*Cos[x]==D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \log \left (e^{4 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )}+1\right )+c_2 \]