Internal problem ID [5380]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 10.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+y(x)=csc(x),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\csc \left (x \right )\right ) \sin \left (x \right )+\left (-x +c_{1} \right ) \cos \left (x \right )+\sin \left (x \right ) c_{2} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 24
DSolve[y''[x]+y[x]==Csc[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (-x+c_1) \cos (x)+\sin (x) (\log (\sin (x))+c_2) \]