Internal problem ID [5560]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.2. THE METHOD OF UNDETERMINED
COEFFICIENTS. Page 67
Problem number: 3(a).
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-4 \cos \left (2 x \right )-6 \cos \relax (x )-8 x^{2}+4 x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.005 (sec). Leaf size: 43
dsolve(diff(y(x),x$2)+4*y(x)=4*cos(2*x)+6*cos(x)+8*x^2-4*x,y(x), singsol=all)
\[ y \relax (x ) = \sin \left (2 x \right ) c_{2}+\cos \left (2 x \right ) c_{1}+2 x \cos \relax (x ) \sin \relax (x )+2 x^{2}+\frac {\left (\cos ^{2}\relax (x )\right )}{2}-\frac {5}{4}+2 \cos \relax (x )-x \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 39
DSolve[y''[x]+4*y[x]==4*Cos[2*x]+6*Cos[x]+8*x^2-4*x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-1) (2 x+1)+2 \cos (x)+\left (\frac {1}{2}+c_1\right ) \cos (2 x)+(x+c_2) \sin (2 x) \\ \end{align*}