Internal problem ID [246]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 51.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\cos \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(x),x$2)+4*y(x)=cos(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {\cos \left (3 x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 28
DSolve[y''[x]+4*y[x]==Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {1}{5} \cos (3 x)+c_1 \cos (2 x)+c_2 \sin (2 x) \]