Internal problem ID [13238]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.5 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-8 y^{\prime \prime \prime }+24 y^{\prime \prime }-32 y^{\prime }+16 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 36
dsolve([diff(y(x),x$4)-8*diff(y(x),x$3)+24*diff(y(x),x$2)-32*diff(y(x),x)+16*y(x)=0,exp(2*x)],y(x), singsol=all)
\[ y = {\mathrm e}^{2 x} c_{1} +x \,{\mathrm e}^{2 x} c_{2} +x^{2} {\mathrm e}^{2 x} c_{3} +x^{3} {\mathrm e}^{2 x} c_{4} \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 28
DSolve[y''''[x]-8*y'''[x]+24*y''[x]-32*y'[x]+16*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{2 x} (x (x (c_4 x+c_3)+c_2)+c_1) \]