75.16.10 problem 483

Internal problem ID [16912]
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 : 483
Date solved : Monday, March 31, 2025 at 03:35:20 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

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

\[ y = \frac {\left (-x +2 c_1 -1\right ) \cos \left (x \right )}{2}-\frac {\sin \left (x \right ) \left (x -2 c_2 \right )}{2} \]

✓ Mathematica. Time used: 0.267 (sec). Leaf size: 62

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

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

✓ Sympy. Time used: 0.094 (sec). Leaf size: 19

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

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