12.19.53 problem section 9.3, problem 53

Internal problem ID [2200]
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 53
Date solved : Monday, January 27, 2025 at 05:43:27 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=4 \,{\mathrm e}^{-x} \left (1-6 x \right )-2 x \cos \left (x \right )+2 \left (1+x \right ) \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 40

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

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

✓ Solution by Mathematica

Time used: 0.419 (sec). Leaf size: 54

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

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