48.3.1 problem Example 3.29

Internal problem ID [7525]
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
Date solved : Monday, January 27, 2025 at 03:04:33 PM
CAS classification : [_Lienard]

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

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ u = \csc \left (x \right ) \left (c_{1} \sin \left (\sqrt {2}\, x \right )+c_{2} \cos \left (\sqrt {2}\, x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 51

DSolve[Sin[x]*D[u[x],{x,2}]+2*Cos[x]*D[u[x],x]+Sin[x]*u[x]==0,u[x],x,IncludeSingularSolutions -> True]
 

\[ u(x)\to \frac {1}{4} e^{-i \sqrt {2} x} \left (4 c_1-i \sqrt {2} c_2 e^{2 i \sqrt {2} x}\right ) \csc (x) \]