81.1.1 problem 1 (a)

Internal problem ID [18596]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter I. Introduction. Exercises at page 13
Problem number : 1 (a)
Date solved : Tuesday, January 28, 2025 at 12:03:28 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }&=c \left ({y^{\prime }}^{2}+1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 24

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

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

✓ Solution by Mathematica

Time used: 4.504 (sec). Leaf size: 21

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

\[ y(x)\to c_2-\frac {\log (\cos (c x+c_1))}{c} \]