12.19.25 problem section 9.3, problem 25

Internal problem ID [2172]
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 25
Date solved : Monday, January 27, 2025 at 05:43:02 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 37

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

\[ y = c_2 \,{\mathrm e}^{-x}+\frac {{\mathrm e}^{x} \left (x^{4}+48 c_4 \,x^{2}+2 x^{3}+48 x c_3 +48 c_1 \right )}{48} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 55

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

\[ y(x)\to \frac {1}{96} e^x \left (2 x^4+4 x^3+(-6+96 c_4) x^2+(6+96 c_3) x-3+96 c_2\right )+c_1 e^{-x} \]