12.19.21 problem section 9.3, problem 21

Internal problem ID [2168]
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 21
Date solved : Monday, January 27, 2025 at 05:43:00 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime }-y&=3 \,{\mathrm e}^{-\frac {x}{2}} \left (1-6 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 50

dsolve(2*diff(y(x),x$4)+1*diff(y(x),x$3)-0*diff(y(x),x$2)-2*diff(y(x),x)-1*y(x)=3*exp(-x/2)*(1-6*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.506 (sec). Leaf size: 63

DSolve[2*D[y[x],{x,4}]+1*D[y[x],{x,3}]-0*D[y[x],{x,2}]-2*D[y[x],x]-1*y[x]==3*Exp[-x/2]*(1-6*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x/2} \left (4 x^2+4 x+c_4 e^{3 x/2}+c_2 \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 \sin \left (\frac {\sqrt {3} x}{2}\right )-8+c_3\right ) \]