12.19.15 problem section 9.3, problem 15

Internal problem ID [2162]
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 15
Date solved : Monday, January 27, 2025 at 05:42:57 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+8 y^{\prime \prime \prime }+24 y^{\prime \prime }+32 y^{\prime }&=-16 \,{\mathrm e}^{-2 x} \left (-x^{3}+x^{2}+x +1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 56

dsolve(diff(y(x),x$4)+8*diff(y(x),x$3)+24*diff(y(x),x$2)+32*diff(y(x),x)=-16*exp(-2*x)*(1+x+x^2-x^3),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.342 (sec). Leaf size: 64

DSolve[D[y[x],{x,4}]+8*D[y[x],{x,3}]+24*D[y[x],{x,2}]+32*D[y[x],x]==-16*Exp[-2*x]*(1+x+x^2-x^3),y[x],x,IncludeSingularSolutions -> True]
 

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