Internal problem ID [13846]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 48.
ODE order: 6.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
\[ \boxed {y^{\left (6\right )}-64 y={\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 62
dsolve(diff(y(x),x$6)-64*y(x)=exp(-2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (-192 c_{3} {\mathrm e}^{3 x}-192 c_{5} {\mathrm e}^{x}\right ) \cos \left (\sqrt {3}\, x \right )+\left (-192 c_{4} {\mathrm e}^{3 x}-192 c_{6} {\mathrm e}^{x}\right ) \sin \left (\sqrt {3}\, x \right )-192 c_{2} {\mathrm e}^{4 x}+x -192 c_{1} \right ) {\mathrm e}^{-2 x}}{192} \]
✓ Solution by Mathematica
Time used: 0.738 (sec). Leaf size: 80
DSolve[y''''''[x]-64*y[x]==Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{768} e^{-2 x} \left (-4 x+768 c_1 e^{4 x}+768 e^x \left (c_2 e^{2 x}+c_3\right ) \cos \left (\sqrt {3} x\right )+768 e^x \left (c_6 e^{2 x}+c_5\right ) \sin \left (\sqrt {3} x\right )-5+768 c_4\right ) \]