53.4.26 problem 28

Internal problem ID [8514]
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 : 28
Date solved : Monday, January 27, 2025 at 04:08:41 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&=1+{y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)=1+diff(y(x),x)^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 2.359 (sec). Leaf size: 16

DSolve[D[y[x],{x,2}]==1+(D[y[x],x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2-\log (\cos (x+c_1)) \]