Internal problem ID [5398]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+5 y=\cos \left (\sqrt {5}\, x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
dsolve(diff(y(x),x$2)+5*y(x)=cos(sqrt(5)*x),y(x), singsol=all)
\[ y = \sin \left (x \sqrt {5}\right ) c_{2} +c_{1} \cos \left (x \sqrt {5}\right )+\frac {\cos \left (x \sqrt {5}\right )}{10}+\frac {\sqrt {5}\, x \sin \left (x \sqrt {5}\right )}{10} \]
✓ Solution by Mathematica
Time used: 0.16 (sec). Leaf size: 45
DSolve[y''[x]+5*y[x]==Cos[Sqrt[5]*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (\frac {1}{20}+c_1\right ) \cos \left (\sqrt {5} x\right )+\frac {1}{10} \left (\sqrt {5} x+10 c_2\right ) \sin \left (\sqrt {5} x\right ) \]