Internal problem ID [5857]
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]
\[ \boxed {\sin \left (x \right ) u^{\prime \prime }+2 \cos \left (x \right ) u^{\prime }+\sin \left (x \right ) u=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 24
dsolve(sin(x)*diff(u(x),x$2)+2*cos(x)*diff(u(x),x)+sin(x)*u(x)=0,u(x), singsol=all)
\[ u \left (x \right ) = \csc \left (x \right ) \left (c_{1} \sin \left (\sqrt {2}\, x \right )+c_{2} \cos \left (\sqrt {2}\, x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.09 (sec). Leaf size: 51
DSolve[Sin[x]*u''[x]+2*Cos[x]*u'[x]+Sin[x]*u[x]==0,u[x],x,IncludeSingularSolutions -> True]
\[ u(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \csc (x) \]