28.1.108 problem 131

Internal problem ID [4414]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 131
Date solved : Monday, January 27, 2025 at 09:15:15 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }&=2 \left (y^{\prime \prime }-1\right ) \cot \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 33

dsolve(diff(y(x),x$3)=2*(diff(y(x),x$2)-1)*cot(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (c_{1} -1\right ) \cos \left (2 x \right )}{8}+\frac {c_{1} x^{2}}{4}+\frac {x^{2}}{4}+c_{2} x -\frac {c_{1}}{8}+c_3 +\frac {1}{8} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 33

DSolve[D[y[x],{x,3}]==2*(D[y[x],{x,2}]-1)*Cot[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} (2+c_1) x^2+c_3 x+\frac {1}{8} c_1 \cos (2 x)+c_2 \]