Internal problem ID [12225]
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]]
\[ \boxed {y^{\left (5\right )}-y^{\prime \prime \prime \prime }+y^{\prime }=2 x^{2}+3} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 372
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 {2 \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )^{2} \left (\frac {3 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} =2\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\left (\frac {3 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} =3\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right ) \left (\frac {3 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} =4\right )}{2}+\left (\frac {3 c_{4} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) x}}{2}+\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right ) \left (x^{3}+\frac {9}{2} x +\frac {3}{2} c_{5} \right )\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )\right )\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )-1\right ) \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =3\right )^{2} \operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )^{2} \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =4\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =2\right )-1\right ) \left (\operatorname {RootOf}\left (\textit {\_Z}^{4}-\textit {\_Z}^{3}+1, \operatorname {index} =1\right )-1\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 182
DSolve[y'''''[x]-y''''[x] +y'[x]==2*x^2+3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,2\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,2\right ]}+\frac {c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,1\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,1\right ]}+\frac {c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,4\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,4\right ]}+\frac {c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,3\right ]\right )}{\text {Root}\left [\text {$\#$1}^4-\text {$\#$1}^3+1\&,3\right ]}+\frac {2 x^3}{3}+3 x+c_5 \]