Internal problem ID [12767]
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: 8.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-3 y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$5)-3*diff(y(x),x$4)+3*diff(y(x),x$3)-3*diff(y(x),x$2)+2*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{2 x}+c_{4} \sin \left (x \right )+c_{5} \cos \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 36
DSolve[y'''''[x]-3*y''''[x]+3*y'''[x]-3*y''[x]+2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^x+\frac {1}{2} c_4 e^{2 x}-c_2 \cos (x)+c_1 \sin (x)+c_5 \]