Internal problem ID [249]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 54.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\csc \left (x \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)+y(x)=csc(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -1-\ln \left (\csc \left (x \right )-\cot \left (x \right )\right ) \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 23
DSolve[y''[x]+y[x]==Csc[x]^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \cos (x) \text {arctanh}(\cos (x))+c_1 \cos (x)+c_2 \sin (x)-1 \]