How to obtain General Solution of Homogenous ODE; (D^2) - (A^2) = 0 in terms of sin & cos

clc;
clear all;
close all;
syms y(x)
O1 = diff(y,x,2) + 600*x == 0;
dsolve(O1)

ans = 

I'm trying this approach but I need output in sin & cos function. Like, as per the equation of motion solution for the same equation, it gives solution as: C1.cos(A.x) + C2.sin(A.x)

[Walter Roberson]

syms C1 C2 A x
eqn = C1*cos(A*x) + C2*sin(A*x)

eqn = 

O1 = diff(eqn, x, 2) + 600 * x

O1 = 

solve(O1 == 0, x)

Warning: Unable to find explicit solution. For options, see help.

 
ans =
 
Empty sym: 0-by-1
 

There is no way that eqn is a solution to that differential equation -- not unless A is 0 or C1 and C2 are 0 (and x is 0)

[Torsten]

Maybe you mean

syms y(x)
O1 = diff(y,x,2) + 600*y == 0;
dsolve(O1)

ans = 

?

Answer 1

[Saurav]

Hello Parvesh,

I understand that you would like the outcome to be expressed in terms of ‘Sine’ and ‘Cos’ after solving a system of differential equation.

I assume that the differential equation you want to solve resembles the standard differential equation of motion given as:-

Instead of reading "" the code needs to be changed to read "" where . This should solve the equation using the “dsolve” function and provide the output in terms of 'sine' and 'cos'.

This is a workaround that can be used:

clc;
clear all;
close all;
syms y(x) x
O1 = diff(y,x,2) + 600*y == 0;
dsolve(O1)

ans = 

I hope this helps!