73.12.21 problem 19.4 (e)

Internal problem ID [15373]
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 (e)
Date solved : Tuesday, January 28, 2025 at 07:53:52 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 33

dsolve(diff(y(x),x$6)-3*diff(y(x),x$4)+3*diff(y(x),x$2)-y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 50

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

\[ y(x)\to e^{-x} \left (x^2 \left (c_6 e^{2 x}+c_3\right )+x \left (c_5 e^{2 x}+c_2\right )+c_4 e^{2 x}+c_1\right ) \]