40.13.5 problem 25

Internal problem ID [6759]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 25
Date solved : Monday, January 27, 2025 at 02:27:43 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-2 \tan \left (x \right ) y^{\prime }-10 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

dsolve(diff(y(x),x$2)-2*tan(x)*diff(y(x),x)-10*y(x)=0,y(x), singsol=all)
 

\[ y = \sec \left (x \right ) \left (c_1 \sinh \left (3 x \right )+c_2 \cosh \left (3 x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]-2*Tan[x]*D[y[x],x]-10*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-3 x} \left (c_2 e^{6 x}+6 c_1\right ) \sec (x) \]