28.2.14 problem 14

Internal problem ID [4457]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 14
Date solved : Monday, January 27, 2025 at 09:18:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-8 y^{\prime }+17 y&={\mathrm e}^{4 x} \left (x^{2}-3 x \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

dsolve(diff(y(x),x$2)-8*diff(y(x),x)+17*y(x)=exp(4*x)*(x^2-3*x*sin(x)),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (\left (3 x^{2}+4 c_{1} \right ) \cos \left (x \right )+\left (-3 x +4 c_{2} \right ) \sin \left (x \right )+4 x^{2}-8\right ) {\mathrm e}^{4 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.235 (sec). Leaf size: 47

DSolve[D[y[x],{x,2}]-8*D[y[x],x]+17*y[x]==Exp[4*x]*(x^2-3*x*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} e^{4 x} \left (8 \left (x^2-2\right )+\left (6 x^2-3+8 c_2\right ) \cos (x)+(-6 x+8 c_1) \sin (x)\right ) \]