Internal problem ID [13431]
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 (a).
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }=12 \,{\mathrm e}^{-2 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 28
dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=12*exp(-2*x),y(x), singsol=all)
\[ y = \frac {c_{1} {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+\frac {{\mathrm e}^{-2 x}}{4}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.152 (sec). Leaf size: 37
DSolve[y''''[x]-4*y'''[x]==12*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^{-2 x}}{4}+\frac {1}{64} c_1 e^{4 x}+x (c_4 x+c_3)+c_2 \]