75.16.56 problem 529

Internal problem ID [17029]
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. Trial and error method. Exercises page 132
Problem number : 529
Date solved : Tuesday, January 28, 2025 at 09:46:40 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 54

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

\[ y(x)\to \sin (x) \int _1^x4 \cos ^2(K[2]) K[2]dK[2]+\cos (x) \int _1^x-2 K[1] \sin (2 K[1])dK[1]+c_1 \cos (x)+c_2 \sin (x) \]