73.15.58 problem 22.12 (c)

Internal problem ID [15489]
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)
Date solved : Tuesday, January 28, 2025 at 07:59:41 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }-4 y^{\prime \prime \prime }&=32 \,{\mathrm e}^{4 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=32*exp(4*x),y(x), singsol=all)
 

\[ y = \frac {\left (32 x +c_{1} -24\right ) {\mathrm e}^{4 x}}{64}+\frac {c_{2} x^{2}}{2}+x c_{3} +c_4 \]

✓ Solution by Mathematica

Time used: 13.095 (sec). Leaf size: 100

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]==32*Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \int _1^x\int _1^{K[3]}\int _1^{K[2]}e^{4 K[1]} (c_1+32 K[1])dK[1]dK[2]dK[3]+x (c_4 x+c_3)+c_2 \\ y(x)\to e^4 \left (-3 x^2+5 x-\frac {17}{8}\right )+\frac {1}{8} e^{4 x} (4 x-3)+x (c_4 x+c_3)+c_2 \\ \end{align*}