83.28.3 problem 3

Internal problem ID [19368]
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 (B) at page 106
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 01:35:36 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Solution by Mathematica

Time used: 0.005 (sec). Leaf size: 17

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

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