Internal problem ID [13214]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.1 (i).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y=25} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 94
dsolve(diff(y(x),x$4)+6*diff(y(x),x$2)+3*diff(y(x),x)-83*y(x)-25=0,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {25}{83}+c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =1\right ) x}+c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =2\right ) x}+c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =3\right ) x}+c_{4} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =4\right ) x} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 117
DSolve[y''''[x]+6*y''[x]+3*y'[x]-83*y[x]-25==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,4\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,1\right ]\right )-\frac {25}{83} \]