73.15.57 problem 22.12 (b)

Internal problem ID [15488]
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 (b)
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 }&=10 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$4)-4*diff(y(x),x$3)=10*sin(2*x),y(x), singsol=all)
 

\[ y = \frac {{\mathrm e}^{4 x} c_{1}}{64}+\frac {c_{2} x^{2}}{2}+\frac {\sin \left (2 x \right )}{8}-\frac {\cos \left (2 x \right )}{4}+x c_{3} +c_4 \]

✓ Solution by Mathematica

Time used: 30.951 (sec). Leaf size: 71

DSolve[D[y[x],{x,4}]-4*D[y[x],{x,3}]==10*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[4]}\int _1^{K[3]}e^{4 K[2]} \left (c_1+\int _1^{K[2]}10 e^{-4 K[1]} \sin (2 K[1])dK[1]\right )dK[2]dK[3]dK[4]+x (c_4 x+c_3)+c_2 \]