73.15.40 problem 22.10 (m)

Internal problem ID [15471]
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 : 22.10 (m)
Date solved : Tuesday, January 28, 2025 at 07:57:47 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=6 \cos \left (x \right )-3 \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 26

dsolve(diff(y(x),x$2)+y(x)=6*cos(x)-3*sin(x),y(x), singsol=all)
 

\[ y = \frac {\left (3 x +2 c_{1} +6\right ) \cos \left (x \right )}{2}+3 \sin \left (x \right ) \left (x +\frac {c_{2}}{3}\right ) \]

✓ Solution by Mathematica

Time used: 0.436 (sec). Leaf size: 66

DSolve[D[y[x],{x,2}]+y[x]==6*Cos[x]-3*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \cos (x) \int _1^x3 \sin (K[1]) (\sin (K[1])-2 \cos (K[1]))dK[1]+\sin (x) \int _1^x3 \cos (K[2]) (2 \cos (K[2])-\sin (K[2]))dK[2]+c_1 \cos (x)+c_2 \sin (x) \]