82.52.3 problem Ex. 3

Internal problem ID [19011]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter IX. Equations of the second order. problems at page 116
Problem number : Ex. 3
Date solved : Tuesday, January 28, 2025 at 12:45:32 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }+5 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-2*tan(x)*diff(y(x),x)+5*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \sec \left (x \right ) \left (c_{1} \sin \left (\sqrt {6}\, x \right )+c_{2} \cos \left (\sqrt {6}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 49

DSolve[D[y[x],{x,2}]-2*Tan[x]*D[y[x],x]+5*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (c_1 e^{-i \sqrt {6} x}-\frac {i c_2 e^{i \sqrt {6} x}}{2 \sqrt {6}}\right ) \sec (x) \]