20.8.8 problem Problem 8

Internal problem ID [3741]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 8
Date solved : Monday, January 27, 2025 at 07:57:17 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y&=100 x \,{\mathrm e}^{x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

dsolve(diff(y(x),x$2)-4*y(x)=100*x*exp(x)*sin(x),y(x), singsol=all)
 

\[ y \left (x \right ) = -10 \,{\mathrm e}^{-2 x} \left (\left (\left (x +\frac {7}{5}\right ) \cos \left (x \right )+\sin \left (x \right ) \left (2 x -\frac {1}{5}\right )\right ) {\mathrm e}^{3 x}-\frac {{\mathrm e}^{4 x} c_{1}}{10}-\frac {c_{2}}{10}\right ) \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 44

DSolve[D[y[x],{x,2}]-4*y[x]==100*x*Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{2 x}+c_2 e^{-2 x}-2 e^x ((10 x-1) \sin (x)+(5 x+7) \cos (x)) \]