73.12.22 problem 19.4 (f)

Internal problem ID [15374]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 19. Arbitrary Homogeneous linear equations with constant coefficients. Additional exercises page 369
Problem number : 19.4 (f)
Date solved : Tuesday, January 28, 2025 at 07:53:52 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-2 y^{\prime \prime \prime }+y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 47

dsolve(diff(y(x),x$6)-2*diff(y(x),x$3)+y(x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {x}{2}} \left (c_6 x +c_4 \right ) \cos \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{-\frac {x}{2}} \left (x c_5 +c_{3} \right ) \sin \left (\frac {\sqrt {3}\, x}{2}\right )+{\mathrm e}^{x} \left (c_{2} x +c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 67

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

\[ y(x)\to e^{-x/2} \left (e^{3 x/2} (c_6 x+c_5)+(c_4 x+c_3) \cos \left (\frac {\sqrt {3} x}{2}\right )+(c_2 x+c_1) \sin \left (\frac {\sqrt {3} x}{2}\right )\right ) \]