12.19.6 problem section 9.3, problem 6

Internal problem ID [2153]
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 6
Date solved : Monday, January 27, 2025 at 05:42:52 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&={\mathrm e}^{x} \left (15 x^{2}+34 x +14\right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 30

dsolve(diff(y(x),x$3)+diff(y(x),x$2)-2*y(x)=exp(x)*(14+34*x+15*x^2),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.113 (sec). Leaf size: 49

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]-2*y[x]==Exp[x]*(14+34*x+15*x^2),y[x],x,IncludeSingularSolutions -> True]
 

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