73.15.53 problem 22.11 (L)

Internal problem ID [15484]
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 (L)
Date solved : Tuesday, January 28, 2025 at 07:59:11 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+20 y&=x^{3} \sin \left (4 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 59

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+20*y(x)=x^3*sin(4*x),y(x), singsol=all)
 

\[ y = \frac {\left (9826 x^{3}+16473 x^{2}+167042 \,{\mathrm e}^{2 x} c_{1} +15810 x +7815\right ) \cos \left (4 x \right )}{167042}+\frac {\left (x^{3}+\frac {3 x^{2}}{17}+68 \,{\mathrm e}^{2 x} c_{2} -\frac {39 x}{578}-\frac {45}{4913}\right ) \sin \left (4 x \right )}{68} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 76

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+20*y[x]==x^3*Sin[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (9826 x^3+1734 x^2-663 x-90\right ) \sin (4 x)+4 \left (9826 x^3+16473 x^2+15810 x+7815\right ) \cos (4 x)}{668168}+c_2 e^{2 x} \cos (4 x)+c_1 e^{2 x} \sin (4 x) \]