Internal problem ID [231]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 23.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=3 x \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+4*y(x)=3*x*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (24 x^{2}+64 c_{2} -3\right ) \sin \left (2 x \right )}{64}+\frac {3 \left (x +\frac {16 c_{1}}{3}\right ) \cos \left (2 x \right )}{16} \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 38
DSolve[y''[x]+4*y[x]==3*x*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} \left (24 x^2-3+64 c_2\right ) \sin (2 x)+\left (\frac {3 x}{16}+c_1\right ) \cos (2 x) \]