73.15.42 problem 22.11 (a)

Internal problem ID [15473]
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 (a)
Date solved : Tuesday, January 28, 2025 at 07:57:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+5 y&=x^{3} {\mathrm e}^{-x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 61

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=x^3*exp(-x)*sin(x),y(x), singsol=all)
 

\[ y = \frac {\left (\left (39546 x^{3}+94302 x^{2}+95160 x +38200\right ) \cos \left (x \right )+59319 \sin \left (x \right ) \left (x^{3}+\frac {18}{13} x^{2}+\frac {138}{169} x +\frac {360}{2197}\right )\right ) {\mathrm e}^{-x}}{771147}+\left (\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} \right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 70

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+5*y[x]==x^3*Exp[-x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-x} \left (\left (39546 x^3+94302 x^2+95160 x+771147 c_2 e^{3 x}+38200\right ) \cos (x)+27 \left (2197 x^3+3042 x^2+1794 x+28561 c_1 e^{3 x}+360\right ) \sin (x)\right )}{771147} \]