12.19.63 problem section 9.3, problem 63

Internal problem ID [2210]
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 63
Date solved : Monday, January 27, 2025 at 05:43:35 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=-2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 37

dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)+1*diff(y(x),x)-0*y(x)=-2*exp(-x)*(7-18*x+6*x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.095 (sec). Leaf size: 42

DSolve[D[y[x],{x,3}]+2*D[y[x],{x,2}]+1*D[y[x],x]-0*y[x]==-2*Exp[-x]*(7-18*x+6*x^2),y[x],x,IncludeSingularSolutions -> True]
 

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