Internal problem ID [13433]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 22. Method of undetermined coefficients. Additional exercises page
412
Problem number: 22.12 (c).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=32 \,{\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=32*exp(4*x),y(x), singsol=all)
\[ y = \frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {{\mathrm e}^{4 x} x}{2}-\frac {3 \,{\mathrm e}^{4 x}}{8}+\frac {c_{2} x^{2}}{2}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.137 (sec). Leaf size: 33
DSolve[y''''[x]-4*y'''[x]==32*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{64} e^{4 x} (32 x-24+c_1)+x (c_4 x+c_3)+c_2 \]