Question

the general solution of ( D² - m²)y = 0 ​

Answer 1

SOLUTION

TO DETERMINE

The general solution of ( D² - m² )y = 0

EVALUATION

Here the given differential equation is

( D² - m² )y = 0

Let $\sf{y = {e}^{nx} }$ be the trial solution

Then the auxiliary equation is

$\sf{ {n}^{2} - {m}^{2} = 0}$

$\sf{ \implies \: (n + m)(n - m)= 0}$

$\sf{ \implies \: n = - m \: , \: m}$

Hence the required general solution is

$\sf{y = a {e}^{ - mx} + b{e}^{ mx} }$

Where a and b are the constants

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ M+N(dy/dx)=0 where M and N are function of

(A) x only

(B) y only

(C) constant

(D) all of these

https://brainly.in/question/38173299

2. This type of equation is of the form dy/dx=f1(x,y)/f2(x,y)

(A) variable seprable

(B) homogeneous

(C) exact

(D) none ...

https://brainly.in/question/38173619