73.9.9 problem 14.1 (i)

Internal problem ID [15270]
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)
Date solved : Tuesday, January 28, 2025 at 07:51:24 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }+6 y^{\prime \prime }+3 y^{\prime }-83 y-25&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = -\frac {25}{83}+c_{1} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =1\right ) x}+c_{2} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =2\right ) x}+c_{3} {\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =3\right ) x}+c_4 \,{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}+6 \textit {\_Z}^{2}+3 \textit {\_Z} -83, \operatorname {index} =4\right ) x} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 117

DSolve[D[y[x],{x,4}]+6*D[y[x],{x,2}]+3*D[y[x],x]-83*y[x]-25==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,3\right ]\right )+c_4 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,4\right ]\right )+c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,2\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^4+6 \text {$\#$1}^2+3 \text {$\#$1}-83\&,1\right ]\right )-\frac {25}{83} \]