12.19.22 problem section 9.3, problem 22

Internal problem ID [2169]
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 22
Date solved : Monday, January 27, 2025 at 05:43:00 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }-5 y^{\prime \prime }+4 y&={\mathrm e}^{x} \left (-3 x^{2}+x +3\right ) \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 39

dsolve(1*diff(y(x),x$4)+0*diff(y(x),x$3)-5*diff(y(x),x$2)-0*diff(y(x),x)+4*y(x)=exp(x)*(3+x-3*x^2),y(x), singsol=all)
 

\[ y = \frac {\left (\left (x^{3}+6 c_1 +x \right ) {\mathrm e}^{3 x}+6 c_3 \,{\mathrm e}^{x}+6 c_4 \,{\mathrm e}^{4 x}+6 c_2 \right ) {\mathrm e}^{-2 x}}{6} \]

✓ Solution by Mathematica

Time used: 0.142 (sec). Leaf size: 51

DSolve[1*D[y[x],{x,4}]+0*D[y[x],{x,3}]-5*D[y[x],{x,2}]-0*D[y[x],x]+4*y[x]==Exp[x]*(3+x-3*x^2),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{36} e^x \left (6 x^3+6 x+7+36 c_3\right )+c_1 e^{-2 x}+c_2 e^{-x}+c_4 e^{2 x} \]