12.19.20 problem section 9.3, problem 20

Internal problem ID [2167]
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 20
Date solved : Monday, January 27, 2025 at 05:42:59 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+y^{\prime \prime \prime }-2 y^{\prime \prime }-6 y^{\prime }-4 y&=-{\mathrm e}^{2 x} \left (15 x^{2}+28 x +4\right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 36

dsolve(1*diff(y(x),x$4)+1*diff(y(x),x$3)-2*diff(y(x),x$2)-6*diff(y(x),x)-4*y(x)=-exp(2*x)*(4+28*x+15*x^2),y(x), singsol=all)
 

\[ y = \left (\cos \left (x \right ) c_3 +c_4 \sin \left (x \right )+c_1 \right ) {\mathrm e}^{-x}-\frac {{\mathrm e}^{2 x} \left (x^{3}-6 c_2 -x \right )}{6} \]

✓ Solution by Mathematica

Time used: 0.159 (sec). Leaf size: 65

DSolve[1*D[y[x],{x,4}]+1*D[y[x],{x,3}]-2*D[y[x],{x,2}]-6*D[y[x],x]-4*y[x]==-Exp[2*x]*(4+28*x+15*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{90} e^{-x} \left (-15 e^{3 x} x^3+15 e^{3 x} x-11 e^{3 x}+90 c_4 e^{3 x}+90 c_2 \cos (x)+90 c_1 \sin (x)+90 c_3\right ) \]