12.19.27 problem section 9.3, problem 27

Internal problem ID [2174]
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 27
Date solved : Monday, January 27, 2025 at 05:43:03 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+3 y^{\prime \prime }+y^{\prime }&={\mathrm e}^{-x} \left (10 x^{2}-24 x +5\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 55

dsolve(1*diff(y(x),x$4)+3*diff(y(x),x$3)+3*diff(y(x),x$2)+1*diff(y(x),x)-0*y(x)=exp(-x)*(5-24*x+10*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (-x^{5}+x^{4}-x^{3}+\left (-6 c_3 -3\right ) x^{2}+\left (-6 c_2 -12 c_3 -6\right ) x -6 c_1 -6 c_2 -12 c_3 -6\right ) {\mathrm e}^{-x}}{6}+c_4 \]

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 65

DSolve[1*D[y[x],{x,4}]+3*D[y[x],{x,3}]+3*D[y[x],{x,2}]+1*D[y[x],x]-0*y[x]==Exp[-x]*(5-24*x+10*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{-x} \left (-x^5+x^4-x^3-3 (1+2 c_3) x^2-6 (1+c_2+2 c_3) x-6 (1+c_1+c_2+2 c_3)\right )+c_4 \]