Internal problem ID [2301]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {y^{\prime \prime }=\sec \left (x \right ) \tan \left (x \right )} \] With initial conditions \begin {align*} \left [y \left (0\right ) = \frac {\pi }{4}, y^{\prime }\left (0\right ) = 1\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve([diff(y(x),x$2)=sec(x)*tan(x),y(0) = 1/4*Pi, D(y)(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = \ln \left (\sec \left (x \right )+\tan \left (x \right )\right )+\frac {\pi }{4} \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 20
DSolve[{y''[x]==Sec[x]*Tan[x],{y[0]==Pi/4,y'[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (8 \text {arctanh}\left (\tan \left (\frac {x}{2}\right )\right )+\pi \right ) \]