67.2.24 problem Problem 3(b)

Internal problem ID [13981]
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)
Date solved : Tuesday, January 28, 2025 at 06:10:58 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 183

dsolve(diff(y(x),x$3)-5*diff(y(x),x$2)+diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} {\mathrm e}^{\frac {\left (\left (116+6 \sqrt {78}\right )^{{2}/{3}}+5 \left (116+6 \sqrt {78}\right )^{{1}/{3}}+22\right ) x}{3 \left (116+6 \sqrt {78}\right )^{{1}/{3}}}}-c_{2} {\mathrm e}^{-\frac {\left (22+\left (116+6 \sqrt {78}\right )^{{2}/{3}}-10 \left (116+6 \sqrt {78}\right )^{{1}/{3}}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{{1}/{3}}}} \sin \left (\frac {\sqrt {3}\, \left (\left (116+6 \sqrt {3}\, \sqrt {26}\right )^{{2}/{3}}-22\right ) x}{6 \left (116+6 \sqrt {3}\, \sqrt {26}\right )^{{1}/{3}}}\right )+c_{3} {\mathrm e}^{-\frac {\left (22+\left (116+6 \sqrt {78}\right )^{{2}/{3}}-10 \left (116+6 \sqrt {78}\right )^{{1}/{3}}\right ) x}{6 \left (116+6 \sqrt {78}\right )^{{1}/{3}}}} \cos \left (\frac {\sqrt {3}\, \left (\left (116+6 \sqrt {3}\, \sqrt {26}\right )^{{2}/{3}}-22\right ) x}{6 \left (116+6 \sqrt {3}\, \sqrt {26}\right )^{{1}/{3}}}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 81

DSolve[D[y[x],{x,3}]-5*D[y[x],{x,2}]+D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-5 \text {$\#$1}^2+\text {$\#$1}-1\&,1\right ]\right ) \]