12.19.65 problem section 9.3, problem 65

Internal problem ID [2212]
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 65
Date solved : Monday, January 27, 2025 at 05:43:36 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime }+y&=-{\mathrm e}^{-x} \left (3 x^{2}-9 x +4\right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 40

dsolve(diff(y(x),x$4)-0*diff(y(x),x$3)-2*diff(y(x),x$2)+0*diff(y(x),x)+y(x)=-exp(-x)*(4-9*x+3*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (-x^{4}+2 x^{3}+16 c_4 x +x^{2}+16 c_2 \right ) {\mathrm e}^{-x}}{16}+{\mathrm e}^{x} \left (x c_3 +c_1 \right ) \]

✓ Solution by Mathematica

Time used: 0.146 (sec). Leaf size: 61

DSolve[D[y[x],{x,4}]-0*D[y[x],{x,3}]-2*D[y[x],{x,2}]+0*D[y[x],x]+1*y[x]==-Exp[-x]*(4-9*x+3*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{32} e^{-x} \left (-2 x^4+4 x^3+2 x^2+x \left (32 c_4 e^{2 x}-2+32 c_2\right )+32 c_3 e^{2 x}-3+32 c_1\right ) \]