Internal problem ID [12765]
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: 6.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve(diff(y(x),x$4)-8*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +c_{2} {\mathrm e}^{2 x}+c_{3} {\mathrm e}^{-x} \sin \left (\sqrt {3}\, x \right )+c_{4} {\mathrm e}^{-x} \cos \left (\sqrt {3}\, x \right ) \]
✓ Solution by Mathematica
Time used: 0.658 (sec). Leaf size: 70
DSolve[y''''[x]-8*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} e^{-x} \left (2 c_1 e^{3 x}-\left (c_2+\sqrt {3} c_3\right ) \cos \left (\sqrt {3} x\right )+\left (\sqrt {3} c_2-c_3\right ) \sin \left (\sqrt {3} x\right )\right )+c_4 \]