40.7.8 problem 17

Internal problem ID [6698]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:24:18 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)+diff(y(x),x)^2+1=0,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: 2.132 (sec). Leaf size: 16

DSolve[D[y[x],{x,2}]+D[y[x],x]^2+1==0,y[x],x,IncludeSingularSolutions -> True]
 

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