2.4 problem Problem 1(d)

Internal problem ID [10877]

Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number: Problem 1(d).
ODE order: 5.
ODE degree: 1.

CAS Maple gives this as type [[_high_order, _missing_y]]

\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }-2 x^{2}-3=0} \]

Solution by Maple

Time used: 0.0 (sec). Leaf size: 154

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

\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right ) x}}{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )}+\frac {c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) x}}{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )}+\frac {c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) x}}{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )}+\frac {c_{4} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x}}{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}+\frac {2 x^{3}}{3}+3 x +c_{5} \]

Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 182

DSolve[y'''''[x]-y''''[x] +y'[x]==2*x^2+3,y[x],x,IncludeSingularSolutions -> True]
 

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