83.38.5 problem 5

Internal problem ID [19464]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (C) at page 133
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 01:45:15 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.146 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)-cot(x)*diff(y(x),x)-sin(x)^2*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 21

DSolve[D[y[x],{x,2}]-Cot[x]*D[y[x],x]-Sin[x]^2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh (\cos (x))-i c_2 \sinh (\cos (x)) \]