15.12.5 problem 5

Internal problem ID [3149]
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 : 5
Date solved : Monday, January 27, 2025 at 07:23:44 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 21

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

\[ y = \frac {\left (3 c_{1} -8 \sin \left (x \right )\right ) \cos \left (x \right )}{3}+c_2 \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.016 (sec). Leaf size: 24

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

\[ y(x)\to -\frac {4}{3} \sin (2 x)+c_1 \cos (x)+c_2 \sin (x) \]