12.19.66 problem section 9.3, problem 66

Internal problem ID [2213]
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 66
Date solved : Monday, January 27, 2025 at 05:43:37 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }-y^{\prime }-2 y&={\mathrm e}^{-2 x} \left (\left (23-2 x \right ) \cos \left (x \right )+\left (8-9 x \right ) \sin \left (x \right )\right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 40

dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=exp(-2*x)*((23-2*x)*cos(x)+(8-9*x)*sin(x)),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 48

DSolve[D[y[x],{x,3}]+2*D[y[x],{x,2}]-D[y[x],x]-2*y[x]==Exp[-2*x]*((23-2*x)*Cos[x]+(8-9*x)*Sin[x]),y[x],x,IncludeSingularSolutions -> True]
 

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