73.15.50 problem 22.11 (i)

Internal problem ID [15481]
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 (i)
Date solved : Tuesday, January 28, 2025 at 07:58:30 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-5 y^{\prime }+6 y&=x^{2} {\mathrm e}^{3 x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 51

dsolve(diff(y(x),x$2)-5*diff(y(x),x)+6*y(x)=x^2*exp(3*x)*sin(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (\left (-50 x^{2}-160 x +109\right ) \cos \left (2 x \right )+\left (-100 x^{2}+130 x +88\right ) \sin \left (2 x \right )+500 c_{2} \right ) {\mathrm e}^{3 x}}{500}+{\mathrm e}^{2 x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]-5*D[y[x],x]+6*y[x]==x^2*Exp[3*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {1}{500} e^{3 x} \left (2 \left (50 x^2-65 x-44\right ) \sin (2 x)+\left (50 x^2+160 x-109\right ) \cos (2 x)\right )+c_1 e^{2 x}+c_2 e^{3 x} \]