15.15.9 problem 10

Internal problem ID [3213]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 10
Date solved : Monday, January 27, 2025 at 07:26:13 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=x \cos \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)=x*cos(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (-2 x -2\right ) \cos \left (2 x \right )}{32}+\frac {\left (3-2 x \right ) \sin \left (2 x \right )}{32}+c_2 x +\frac {{\mathrm e}^{-2 x} c_{1}}{4}+c_3 \]

✓ Solution by Mathematica

Time used: 1.598 (sec). Leaf size: 48

DSolve[D[y[x],{x,3}]+2*D[y[x],{x,2}]==x*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 x+\frac {1}{16} \left (-x \sin (2 x)-(x+1) \cos (2 x)+4 c_1 e^{-2 x}+3 \sin (x) \cos (x)\right )+c_2 \]