Internal problem ID [13766]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.14 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=25 x \cos \left (2 x \right )+3 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+9*y(x)=25*x*cos(2*x)+3*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (2 c_{1} -x \right ) \cos \left (3 x \right )}{2}+\frac {\left (1+12 c_{2} \right ) \sin \left (3 x \right )}{12}+5 \cos \left (2 x \right ) x +4 \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.274 (sec). Leaf size: 39
DSolve[y''[x]+9*y[x]==25*x*Cos[2*x]+3*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 4 \sin (2 x)+5 x \cos (2 x)+\left (-\frac {x}{2}+c_1\right ) \cos (3 x)+c_2 \sin (3 x) \]