40.14.1 problem 22

Internal problem ID [6772]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 22
Date solved : Monday, January 27, 2025 at 02:30:07 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: 0.006 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)+diff(y(x),x)^2+1=0,y(x), singsol=all)
 

\[ y = \ln \left (-\sin \left (x \right ) c_1 +\cos \left (x \right ) c_2 \right ) \]

✓ Solution by Mathematica

Time used: 2.400 (sec). Leaf size: 16

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

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