75.17.7 problem 557

Internal problem ID [17056]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Chapter 2 (Higher order ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Superposition principle. Exercises page 137
Problem number : 557
Date solved : Tuesday, January 28, 2025 at 09:47:54 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

Solution by Maple

Time used: 0.004 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)+4*y(x)=sin(x)*sin(2*x),y(x), singsol=all)
 
\[ y = \sin \left (2 x \right ) c_{2} +\cos \left (2 x \right ) c_{1} -\frac {2 \cos \left (x \right )}{15}+\frac {2 \cos \left (x \right )^{3}}{5} \]

Solution by Mathematica

Time used: 0.073 (sec). Leaf size: 68

DSolve[D[y[x],{x,2}]+4*y[x]==Sin[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to \sin (2 x) \int _1^x\frac {1}{4} \sin (K[2]) \sin (4 K[2])dK[2]+\cos (2 x) \int _1^x-2 \cos ^2(K[1]) \sin ^3(K[1])dK[1]+c_1 \cos (2 x)+c_2 \sin (2 x) \]