Internal problem ID [13491]
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: 13.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\left (5\right )}-6 y^{\prime \prime \prime \prime }+13 y^{\prime \prime \prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 34
dsolve(diff(y(x),x$5)-6*diff(y(x),x$4)+13*diff(y(x),x$3)=0,y(x), singsol=all)
\[ y = c_{1} +c_{2} x +c_{3} x^{2}+c_{4} {\mathrm e}^{3 x} \sin \left (2 x \right )+c_{5} \cos \left (2 x \right ) {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 2.104 (sec). Leaf size: 56
DSolve[y'''''[x]-6*y''''[x]+13*y'''[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_5 x^2+c_4 x-\frac {e^{3 x} ((46 c_1+9 c_2) \cos (2 x)+(9 c_1-46 c_2) \sin (2 x))}{2197}+c_3 \]