12.19.29 problem section 9.3, problem 29

Internal problem ID [2176]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 29
Date solved : Monday, January 27, 2025 at 05:43:04 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{-x} \left (\left (16+10 x \right ) \cos \left (x \right )+\left (30-10 x \right ) \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 40

dsolve(0*diff(y(x),x$4)+1*diff(y(x),x$3)-1*diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=exp(-x)*((16+10*x)*cos(x)+(30-10*x)*sin(x)),y(x), singsol=all)
 

\[ y = \left (c_1 \,{\mathrm e}^{3 x}+c_3 \,{\mathrm e}^{4 x}+\left (\left (x +1\right ) \cos \left (x \right )-\sin \left (x \right ) \left (x -2\right )\right ) {\mathrm e}^{x}+c_2 \right ) {\mathrm e}^{-2 x} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 49

DSolve[0*D[y[x],{x,4}]+1*D[y[x],{x,3}]-1*D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==Exp[-x]*((16+10*x)*Cos[x]+(30-10*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (-e^x (x-2) \sin (x)+e^x (x+1) \cos (x)+c_2 e^{3 x}+c_3 e^{4 x}+c_1\right ) \]