77.14.1 problem 1

Internal problem ID [20465]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (F) at page 42
Problem number : 1
Date solved : Thursday, October 02, 2025 at 06:03:07 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (2 x \right )+\sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)+9*y(x) = cos(2*x)+sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 +\frac {\cos \left (2 x \right )}{5}+\frac {\sin \left (2 x \right )}{5} \]

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 34

ode=D[y[x],{x,2}]+9*y[x]==Cos[2*x]+Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{5} (\sin (2 x)+\cos (2 x)+5 c_1 \cos (3 x)+5 c_2 \sin (3 x)) \end{align*}

✓ Sympy. Time used: 0.048 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(9*y(x) - sin(2*x) - cos(2*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (3 x \right )} + C_{2} \cos {\left (3 x \right )} + \frac {\sin {\left (2 x \right )}}{5} + \frac {\cos {\left (2 x \right )}}{5} \]