73.15.49 problem 22.11 (h)

Internal problem ID [15480]
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 : 22.11 (h)
Date solved : Tuesday, January 28, 2025 at 07:58:27 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=x^{2} \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 49

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*cos(2*x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{3 x} c_{2} +{\mathrm e}^{2 x} c_{1} +\frac {\left (676 x^{2}-2080 x -1909\right ) \cos \left (2 x \right )}{35152}+\frac {\left (-3380 x^{2}-3796 x -725\right ) \sin \left (2 x \right )}{35152} \]

✓ Solution by Mathematica

Time used: 0.029 (sec). Leaf size: 58

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==x^2*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (676 x^2-2080 x-1909\right ) \cos (2 x)-\left (3380 x^2+3796 x+725\right ) \sin (2 x)}{35152}+c_1 e^{2 x}+c_2 e^{3 x} \]