12.19.30 problem section 9.3, problem 30

Internal problem ID [2177]
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 30
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 (1-22 x \right ) \cos \left (2 x \right )-\left (1+6 x \right ) \sin \left (2 x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 50

dsolve(1*diff(y(x),x$3)+1*diff(y(x),x$2)-4*diff(y(x),x)-4*y(x)=exp(-x)*((1-22*x)*cos(2*x)-(1+6*x)*sin(2*x)),y(x), singsol=all)
 

\[ y = -{\mathrm e}^{-2 x} \left ({\mathrm e}^{x} \left (x -1\right ) \cos \left (2 x \right )-\left (x +1\right ) {\mathrm e}^{x} \sin \left (2 x \right )-c_3 \,{\mathrm e}^{4 x}+\left (-c_2 +\frac {5}{3}\right ) {\mathrm e}^{x}-c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 51

DSolve[1*D[y[x],{x,3}]+1*D[y[x],{x,2}]-4*D[y[x],x]-4*y[x]==Exp[-x]*((1-22*x)*Cos[2*x]-(1+6*x)*Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

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