56.4.72 problem 69

Internal problem ID [8961]
Book : Own collection of miscellaneous problems
Section : section 4.0
Problem number : 69
Date solved : Monday, January 27, 2025 at 05:22:41 PM
CAS classification : [[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.162 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)*sin(2*x)^2+diff(y(x),x)*sin(4*x)-4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 29

DSolve[D[y[x],{x,2}]*Sin[2*x]^2+D[y[x],x]*Sin[4*x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {c_1-i c_2 \cos (2 x)}{\sqrt {\sin ^2(2 x)}} \]