Internal problem ID [5104]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.29.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Lienard]
Solve \begin {gather*} \boxed {\sin \relax (x ) u^{\prime \prime }+2 \cos \relax (x ) u^{\prime }+\sin \relax (x ) u=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 29
dsolve(sin(x)*diff(u(x),x$2)+2*cos(x)*diff(u(x),x)+sin(x)*u(x)=0,u(x), singsol=all)
\[ u \relax (x ) = \frac {c_{1} \sin \left (x \sqrt {2}\right )}{\sin \relax (x )}+\frac {c_{2} \cos \left (x \sqrt {2}\right )}{\sin \relax (x )} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 51
DSolve[Sin[x]*u''[x]+2*Cos[x]*u'[x]+Sin[x]*u[x]==0,u[x],x,IncludeSingularSolutions -> True]
\begin{align*} u(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \csc (x) \\ \end{align*}