12.19.58 problem section 9.3, problem 58

Internal problem ID [2205]
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 58
Date solved : Monday, January 27, 2025 at 05:43:32 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+5 y^{\prime \prime \prime }+9 y^{\prime \prime }+7 y^{\prime }+2 y&={\mathrm e}^{-x} \left (30+24 x \right )-{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(x),x$4)+5*diff(y(x),x$3)+9*diff(y(x),x$2)+7*diff(y(x),x)+2*y(x)=exp(-x)*(30+24*x)-exp(-2*x),y(x), singsol=all)
 

\[ y = \left (x^{4}+x^{3}+\left (c_4 -3\right ) x^{2}+\left (c_3 +6\right ) x +c_2 -6\right ) {\mathrm e}^{-x}+{\mathrm e}^{-2 x} \left (x +c_1 +3\right ) \]

✓ Solution by Mathematica

Time used: 0.299 (sec). Leaf size: 44

DSolve[D[y[x],{x,4}]+5*D[y[x],{x,3}]+9*D[y[x],{x,2}]+7*D[y[x],x]+2*y[x]==Exp[-x]*(30+24*x)-Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^x \left (x^4+x^3+(-3+c_4) x^2+(6+c_3) x-6+c_2\right )+x+3+c_1\right ) \]