58.2.22 problem 23

Internal problem ID [9145]
Book : Second order enumerated odes
Section : section 2
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:49:01 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+\tan \left (x \right ) y^{\prime }+\cos \left (x \right )^{2} y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)+tan(x)*diff(y(x),x)+cos(x)^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.833 (sec). Leaf size: 37

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

\[ y(x)\to c_1 \cosh \left (\sqrt {-\sin ^2(x)}\right )+i c_2 \sinh \left (\sqrt {-\sin ^2(x)}\right ) \]