75.13.1 problem 318

Internal problem ID [16835]
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 : Monday, March 31, 2025 at 03:23:49 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+y(x) = 2*cos(x)+2*sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (c_1 -x +1\right ) \cos \left (x \right )+\sin \left (x \right ) \left (x +c_2 \right ) \]

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

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

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

✓ Sympy. Time used: 0.113 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*sin(x) - 2*cos(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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