7.11.15 problem 15

Internal problem ID [336]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 15
Date solved : Monday, January 27, 2025 at 02:45:43 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (5\right )}+5 y^{\prime \prime \prime \prime }-y&=17 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 101

dsolve(diff(y(x),x$5)+5*diff(y(x),x$4)-y(x)=17,y(x), singsol=all)
 

\[ y = -17+c_1 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =1\right ) x}+c_2 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =2\right ) x}+c_3 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =4\right ) x}+c_5 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{5}+5 \textit {\_Z}^{4}-1, \operatorname {index} =5\right ) x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 122

DSolve[D[y[x],{x,5}]+5*D[y[x],{x,4}]-y[x]==17,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,4\right ]\right )+c_5 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,5\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,3\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^5+5 \text {$\#$1}^4-1\&,1\right ]\right )-17 \]