12.19.7 problem section 9.3, problem 7

Internal problem ID [2154]
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 7
Date solved : Monday, January 27, 2025 at 05:42:53 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{-2 x} \left (1-15 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 34

dsolve(4*diff(y(x),x$3)+8*diff(y(x),x$2)-diff(y(x),x)-2*y(x)=-exp(-2*x)*(1-15*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.076 (sec). Leaf size: 53

DSolve[4*D[y[x],{x,3}]+8*D[y[x],{x,2}]-D[y[x],x]-2*y[x]==-Exp[-2*x]*(1-15*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{10} e^{-2 x} \left (5 x^2+10 x+2 \left (5 c_1 e^{3 x/2}+5 c_2 e^{5 x/2}+4+5 c_3\right )\right ) \]