75.13.1 problem 318

Internal problem ID [16906]
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 13. Basic concepts and definitions. Exercises page 98
Problem number : 318
Date solved : Tuesday, January 28, 2025 at 09:40:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

Time used: 0.279 (sec). Leaf size: 60

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

\[ y(x)\to \cos (x) \int _1^x-2 \sin (K[1]) (\cos (K[1])+\sin (K[1]))dK[1]+\sin (x) \int _1^x2 \cos (K[2]) (\cos (K[2])+\sin (K[2]))dK[2]+c_1 \cos (x)+c_2 \sin (x) \]