83.32.4 problem 4

Internal problem ID [19403]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Exercise VII (F) at page 113
Problem number : 4
Date solved : Tuesday, January 28, 2025 at 01:37:57 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 17

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

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

✓ Solution by Mathematica

Time used: 1.727 (sec). Leaf size: 16

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

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