12.19.1 problem section 9.3, problem 1

Internal problem ID [2148]
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 1
Date solved : Monday, January 27, 2025 at 05:42:50 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-6 y^{\prime \prime }+11 y^{\prime }-6 y&=-{\mathrm e}^{x} \left (-24 x^{2}+76 x +4\right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 32

dsolve(diff(y(x),x$3)-6*diff(y(x),x$2)+11*diff(y(x),x)-6*y(x)=-exp(x)*(4+76*x-24*x^2),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} \left (c_3 \,{\mathrm e}^{2 x}+4 x^{3}+c_2 \,{\mathrm e}^{x}-x^{2}+c_1 -17 x \right ) \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 47

DSolve[D[y[x],{x,3}]-6*D[y[x],{x,2}]+11*D[y[x],x]-6*y[x]==-Exp[x]*(4+76*x-24*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^x \left (8 x^3-2 x^2-34 x+2 c_2 e^x+2 c_3 e^{2 x}-49+2 c_1\right ) \]