12.19.28 problem section 9.3, problem 28

Internal problem ID [2175]
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 28
Date solved : Monday, January 27, 2025 at 05:43:03 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-7 y^{\prime \prime \prime }+18 y^{\prime \prime }-20 y^{\prime }+8 y&={\mathrm e}^{2 x} \left (-5 x^{2}-8 x +3\right ) \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 42

dsolve(1*diff(y(x),x$4)-7*diff(y(x),x$3)+18*diff(y(x),x$2)-20*diff(y(x),x)+8*y(x)=exp(2*x)*(3-8*x-5*x^2),y(x), singsol=all)
 

\[ y = -\frac {\left (\left (x^{5}-x^{4}-12 c_3 \,x^{2}-2 x^{3}-12 c_4 x -12 c_2 \right ) {\mathrm e}^{x}-12 c_1 \right ) {\mathrm e}^{x}}{12} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 59

DSolve[1*D[y[x],{x,4}]-7*D[y[x],{x,3}]+18*D[y[x],{x,2}]-20*D[y[x],x]+8*y[x]==Exp[2*x]*(3-8*x-5*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} e^{2 x} \left (-x^5+x^4+2 x^3+6 (-1+2 c_4) x^2+12 (1+c_3) x+12 (-1+c_2)\right )+c_1 e^x \]