Internal problem ID [11796]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.3. The method of undetermined coefficients. Exercises page
151
Problem number: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=12 x^{2}-16 x \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 37
dsolve(diff(y(x),x$2)+4*y(x)=12*x^2-16*x*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {3}{2}+\frac {\left (-8 x^{2}+4 c_{2} +1\right ) \sin \left (2 x \right )}{4}+\left (c_{1} -x \right ) \cos \left (2 x \right )+3 x^{2} \]
✓ Solution by Mathematica
Time used: 0.251 (sec). Leaf size: 44
DSolve[y''[x]+4*y[x]==12*x^2-16*x*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 3 x^2+\frac {1}{4} \left (-8 x^2+1+4 c_2\right ) \sin (2 x)+(-x+c_1) \cos (2 x)-\frac {3}{2} \]