28.2.40 problem 40

Internal problem ID [4483]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 40
Date solved : Tuesday, March 04, 2025 at 06:48:06 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=2 \sin \left (x \right )-3 \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=diff(diff(y(x),x),x)+y(x) = 2*sin(x)-3*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+y[x]==2*Sin[x]-3*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \cos (2 x)+(-x+c_1) \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.095 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*sin(x) + 3*cos(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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