12.19.19 problem section 9.3, problem 19

Internal problem ID [2166]
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 19
Date solved : Monday, January 27, 2025 at 05:42:59 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 34

dsolve(2*diff(y(x),x$4)+5*diff(y(x),x$3)+0*diff(y(x),x$2)-5*diff(y(x),x)-2*y(x)=18*exp(x)*(5+2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 48

DSolve[2*D[y[x],{x,4}]+5*D[y[x],{x,3}]+0*D[y[x],{x,2}]-5*D[y[x],x]-2*y[x]==18*Exp[x]*(5+2*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x} \left (e^{3 x} \left (x^2+2 x-\frac {40}{9}+c_4\right )+c_1 e^{3 x/2}+c_3 e^x+c_2\right ) \]