Internal problem ID [6540]
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)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime } \left (\sin ^{2}\left (2 x \right )\right )+y^{\prime } \sin \left (4 x \right )-4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 37
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)
\[ y \relax (x ) = \frac {c_{1}}{\sqrt {-2 \cos \left (4 x \right )+2}}+\frac {c_{2} \sqrt {\cos \left (4 x \right )+1}}{\sqrt {-2 \cos \left (4 x \right )+2}} \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 23
DSolve[y''[x]*Sin[2*x]^2+y'[x]*Sin[4*x]-4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \csc (2 x) (c_1-i c_2 \cos (2 x)) \\ \end{align*}