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

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Parvesh Deepan
Parvesh Deepan 2024-2-26
回答： Saurav 2024-3-7
Ran in:
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)
  2 个评论
Walter Roberson
Walter Roberson 2024-2-26
Ran in:
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)

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回答（1 个）

Saurav
Saurav 2024-3-7
Ran in:
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!

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