Internal problem ID [13486]
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: 8.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x$4)-8*diff(y(x),x$2)+16*y(x)=0,y(x), singsol=all)
\[ y = c_{1} {\mathrm e}^{-2 x}+c_{2} x \,{\mathrm e}^{-2 x}+{\mathrm e}^{2 x} c_{3} +x \,{\mathrm e}^{2 x} c_{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 35
DSolve[y''''[x]-8*y''[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-2 x} \left (c_3 e^{4 x}+x \left (c_4 e^{4 x}+c_2\right )+c_1\right ) \]