71.11.2 problem 2

Internal problem ID [14511]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:42:50 AM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime \prime }+4 y^{\prime \prime }&=24 x^{2}-6 x +14+32 \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 48

dsolve(diff(y(x),x$4)+4*diff(y(x),x$2)=24*x^2-6*x+14+32*cos(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (-c_{1} -10\right ) \cos \left (2 x \right )}{4}+\frac {\left (-c_{2} -8 x \right ) \sin \left (2 x \right )}{4}+\frac {x^{4}}{2}-\frac {x^{3}}{4}+\frac {x^{2}}{4}+c_{3} x +c_4 \]

✓ Solution by Mathematica

Time used: 60.195 (sec). Leaf size: 123

DSolve[D[y[x],{x,4}]+4*D[y[x],{x,2}]==24*x^2-6*x+14+32*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\int _1^{K[4]}\left (c_1 \cos (2 K[3])+\int _1^{K[3]}-\left (\left (12 K[1]^2-3 K[1]+16 \cos (2 K[1])+7\right ) \sin (2 K[1])\right )dK[1] \cos (2 K[3])+c_2 \sin (2 K[3])+\sin (2 K[3]) \int _1^{K[3]}\cos (2 K[2]) \left (12 K[2]^2-3 K[2]+16 \cos (2 K[2])+7\right )dK[2]\right )dK[3]dK[4]+c_4 x+c_3 \]