Internal problem ID [13317]
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).
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (6\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime }-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
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)
\[ y = c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{x} x +c_{3} {\mathrm e}^{x} x^{2}+c_{4} {\mathrm e}^{-x}+c_{5} {\mathrm e}^{-x} x +c_{6} {\mathrm e}^{-x} x^{2} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 50
DSolve[y''''''[x]-3*y''''[x]+3*y''[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (x^2 \left (c_6 e^{2 x}+c_3\right )+x \left (c_5 e^{2 x}+c_2\right )+c_4 e^{2 x}+c_1\right ) \]