73.15.56 problem 22.12 (a)

Internal problem ID [15487]
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)
Date solved : Tuesday, January 28, 2025 at 07:59:40 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=12 \,{\mathrm e}^{-2 x} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 28

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=12*exp(-2*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 x} c_{1}}{64}+\frac {c_{2} x^{2}}{2}+\frac {{\mathrm e}^{-2 x}}{4}+x c_{3} +c_4 \]

✓ Solution by Mathematica

Time used: 0.148 (sec). Leaf size: 37

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]==12*Exp[-2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {e^{-2 x}}{4}+\frac {1}{64} c_1 e^{4 x}+x (c_4 x+c_3)+c_2 \]