12.19.17 problem section 9.3, problem 17

Internal problem ID [2164]
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 17
Date solved : Monday, January 27, 2025 at 05:42:58 AM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 101

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

\[ y = c_1 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =1\right ) x}+c_2 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =2\right ) x}+c_3 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+3 \textit {\_Z} -1, \operatorname {index} =4\right ) x}+{\mathrm e}^{x} \left (x +1\right )^{2} \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 123

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

\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,4\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-2 \text {$\#$1}^3+3 \text {$\#$1}-1\&,1\right ]\right )+e^x (x+1)^2 \]