83.48.12 problem Ex 12 page 107

Internal problem ID [19604]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter VII. Exact differential equations.
Problem number : Ex 12 page 107
Date solved : Tuesday, January 28, 2025 at 02:03:55 PM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x$2)=sec(x)^2,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}]==Sec[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

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