Internal problem ID [6313]
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]]
\[ \boxed {y^{\prime \prime }+4 y=4 \cos \left (2 x \right )+6 \cos \left (x \right )+8 x^{2}-4 x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
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)
\[ y \left (x \right ) = -1+\frac {\left (4 c_{1} +1\right ) \cos \left (2 x \right )}{4}+\left (x +c_{2} \right ) \sin \left (2 x \right )+2 x^{2}-x +2 \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.515 (sec). Leaf size: 43
DSolve[y''[x]+4*y[x]==4*Cos[2*x]+6*Cos[x]+8*x^2-4*x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 2 x^2-x+x \sin (2 x)+2 \cos (x)+\left (\frac {1}{2}+c_1\right ) \cos (2 x)+c_2 \sin (2 x)-1 \]