Internal problem ID [2309]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.9, Reduction of Order. page
572
Problem number: Problem 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-\csc \left (x \right )=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \sin \left (x \right ) \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 25
dsolve([diff(y(x),x$2)+y(x)=csc(x),sin(x)],y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +c_{1} \cos \left (x \right )-\ln \left (\csc \left (x \right )\right ) \sin \left (x \right )-\cos \left (x \right ) x \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 27
DSolve[y''[x]+y[x]==Csc[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (-x+c_1) \cos (x)+\sin (x) (\log (\tan (x))+\log (\cos (x))+c_2) \\ \end{align*}