Internal problem ID [10897]
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 3(b).
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 181
dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\left (\left (116+6 \sqrt {78}\right )^{\frac {2}{3}}+5 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}+22\right ) x}{3 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}}-c_{2} {\mathrm e}^{-\frac {\left (22+\left (116+6 \sqrt {78}\right )^{\frac {2}{3}}-10 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}} \sin \left (\frac {\left (\sqrt {3}\, \left (116+6 \sqrt {78}\right )^{\frac {2}{3}}-22 \sqrt {3}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}\right )+c_{3} {\mathrm e}^{-\frac {\left (22+\left (116+6 \sqrt {78}\right )^{\frac {2}{3}}-10 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}} \cos \left (\frac {\left (\sqrt {3}\, \left (116+6 \sqrt {78}\right )^{\frac {2}{3}}-22 \sqrt {3}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{\frac {1}{3}}}\right ) \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 81
DSolve[y'''[x]-5*y''[x]+y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]\right ) \\ \end{align*}