40.11.6 problem 31

Internal problem ID [6740]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary problems. Page 107
Problem number : 31
Date solved : Monday, January 27, 2025 at 02:26:54 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 24

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

\[ y = \frac {\left (4 c_1 -x \right ) \cos \left (2 x \right )}{4}+\sin \left (2 x \right ) c_2 \]

✓ Solution by Mathematica

Time used: 0.058 (sec). Leaf size: 33

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

\[ y(x)\to \left (-\frac {x}{4}+c_1\right ) \cos (2 x)+\frac {1}{8} (1+16 c_2) \sin (x) \cos (x) \]