Internal problem ID [5378]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 14. Linear equations with constant coefficients. Supplemetary problems. Page
92
Problem number: 21.
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: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)+y(x)=csc(x),y(x), singsol=all)
\[ y = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} -\ln \left (\csc \left (x \right )\right ) \sin \left (x \right )-x \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.082 (sec). Leaf size: 86
DSolve[y''[x]-y[x]==Csc[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {1}{2}+\frac {i}{2}\right ) e^{i x} \left (\operatorname {Hypergeometric2F1}\left (\frac {1}{2}-\frac {i}{2},1,\frac {3}{2}-\frac {i}{2},e^{2 i x}\right )+i \operatorname {Hypergeometric2F1}\left (\frac {1}{2}+\frac {i}{2},1,\frac {3}{2}+\frac {i}{2},e^{2 i x}\right )\right )+c_1 e^x+c_2 e^{-x} \]