Internal problem ID [12764]
Book: Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section: Chapter 4. N-th Order Linear Differential Equations. Exercises 4.3, page 210
Problem number: 5.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }+8 y^{\prime \prime }-8 y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)+8*diff(y(x),x$2)-8*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \left (\left (c_{4} x +c_{2} \right ) \cos \left (x \right )+\sin \left (x \right ) \left (c_{3} x +c_{1} \right )\right ) {\mathrm e}^{x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 30
DSolve[y''''[x]-4*y'''[x]+8*y''[x]-8*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x ((c_4 x+c_3) \cos (x)+(c_2 x+c_1) \sin (x)) \]