49.6.7 problem 1(g)

Internal problem ID [7635]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 69
Problem number : 1(g)
Date solved : Monday, January 27, 2025 at 03:08:38 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 33

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

\[ y(x)\to \frac {1}{8} (\cos (3 x)+(-1+8 c_1) \cos (x)+4 (x+2 c_2) \sin (x)) \]