83.38.6 problem 6

Internal problem ID [19465]
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 : 6
Date solved : Tuesday, January 28, 2025 at 01:45:19 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

\[ y \left (x \right ) = c_{1} \left (\csc \left (x \right )+\cot \left (x \right )\right )^{-i}+c_{2} \left (\csc \left (x \right )+\cot \left (x \right )\right )^{i} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 21

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

\[ y(x)\to c_1 \cos (\text {arctanh}(\cos (x)))-c_2 \sin (\text {arctanh}(\cos (x))) \]