7.11.52 problem 54

Internal problem ID [373]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 54
Date solved : Wednesday, February 05, 2025 at 03:26:19 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=\csc \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+y(x)=csc(x)^2,y(x), singsol=all)
 

\[ y = c_2 \sin \left (x \right )+\cos \left (x \right ) c_1 -1-\ln \left (\csc \left (x \right )-\cot \left (x \right )\right ) \cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.031 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]+y[x]==Csc[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \text {arctanh}(\cos (x))+c_1 \cos (x)+c_2 \sin (x)-1 \]