15.12.6 problem 6

Internal problem ID [3150]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 6
Date solved : Monday, January 27, 2025 at 07:23:46 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=2 x -2 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 25

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

\[ y = \frac {\left (x +2 c_{1} \right ) \cos \left (2 x \right )}{2}+\sin \left (2 x \right ) c_2 +\frac {x}{2} \]

✓ Solution by Mathematica

Time used: 0.125 (sec). Leaf size: 30

DSolve[D[y[x],{x,2}]+4*y[x]==2*(x-Sin[2*x]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} (x+(x+2 c_1) \cos (2 x)+2 c_2 \sin (2 x)) \]