Internal problem ID [7293]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 69.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {y^{\prime \prime } \sin \left (2 x \right )^{2}+y^{\prime } \sin \left (4 x \right )-4 y=0} \]
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = c_{1} \csc \left (2 x \right )+\cot \left (2 x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 29
DSolve[y''[x]*Sin[2*x]^2+y'[x]*Sin[4*x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_1-i c_2 \cos (2 x)}{\sqrt {\sin ^2(2 x)}} \]