Internal problem ID [6081]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime } \cos \relax (x )-y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)*cos(x)=diff(y(x),x),y(x), singsol=all)
\[ y \relax (x ) = c_{1}+\left (\ln \left (\frac {1+\sin \relax (x )}{\cos \relax (x )}\right )-\ln \left (\cos \relax (x )\right )\right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.146 (sec). Leaf size: 25
DSolve[y''[x]*Cos[x]==y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \log \left (e^{4 \tanh ^{-1}\left (\tan \left (\frac {x}{2}\right )\right )}+1\right )+c_2 \\ \end{align*}