23.3.2 problem 7(b)

Internal problem ID [4143]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 7(b)
Date solved : Monday, January 27, 2025 at 08:40:00 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-12 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 151

dsolve(diff(y(x),x$3)-diff(y(x),x$2)-12*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} {\mathrm e}^{\frac {\left (\left (163+18 \sqrt {82}\right )^{{2}/{3}}+\left (163+18 \sqrt {82}\right )^{{1}/{3}}+1\right ) x}{3 \left (163+18 \sqrt {82}\right )^{{1}/{3}}}}-c_{2} {\mathrm e}^{-\frac {\left (\left (163+18 \sqrt {82}\right )^{{1}/{3}}-1\right )^{2} x}{6 \left (163+18 \sqrt {82}\right )^{{1}/{3}}}} \sin \left (\frac {\sqrt {3}\, \left (\left (163+18 \sqrt {82}\right )^{{2}/{3}}-1\right ) x}{6 \left (163+18 \sqrt {82}\right )^{{1}/{3}}}\right )+c_3 \,{\mathrm e}^{-\frac {\left (\left (163+18 \sqrt {82}\right )^{{1}/{3}}-1\right )^{2} x}{6 \left (163+18 \sqrt {82}\right )^{{1}/{3}}}} \cos \left (\frac {\sqrt {3}\, \left (\left (163+18 \sqrt {82}\right )^{{2}/{3}}-1\right ) x}{6 \left (163+18 \sqrt {82}\right )^{{1}/{3}}}\right ) \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 75

DSolve[D[y[x],{x,3}]-D[y[x],{x,2}]-12*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_2 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-12\&,2\right ]\right )+c_3 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-12\&,3\right ]\right )+c_1 \exp \left (x \text {Root}\left [\text {$\#$1}^3-\text {$\#$1}^2-12\&,1\right ]\right ) \]