Internal problem ID [5245]
Book: An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY
1961
Section: Chapter 2. Linear equations with constant coefficients. Page 93
Problem number: 1(b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+4 y-\sin \left (2 x \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$2)+4*y(x)=sin(2*x),y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}-\frac {x \cos \left (2 x \right )}{4} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 33
DSolve[y''[x]+4*y[x]==Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \left (-\frac {x}{4}+c_1\right ) \cos (2 x)+\frac {1}{8} (1+16 c_2) \sin (x) \cos (x) \\ \end{align*}