kendiee123
contestada

what is the general solution to the differential equation dy/dx= cos(8x)/cos(4y) ?
A. sin =(4y) - sin(8x) = C
B. sin (4y) - 2 sin(8x) = C
C. 2 sin(4y) - sin(8x) = C
D. 2 tan(4y) - sin(8x) = C

Respuesta :

abidemiokin

Answer:

2sin4y - sin8x = K (C)

Step-by-step explanation:

Given the differential equation

dy/dx= cos(8x)/cos(4y)

This can be solved by using the variable separable method.

Step 1;

Separate the variables

Cos4ydy = cos 8xdx

step 2:

Integrate both sides of the equation

∫cos4y dy = ∫cos8x dx

sin4y/4 = sin8x/8

Step 3:

Add constant of integration to the side containing x variable

sin4y/4 = sin8x/8+ C

Taking sin8x to the other side we have:

sin4y/4-sin8x/8 = C

Multiplying through by 8:

2sin4y - sin8x = 8C

2sin4y - sin8x = K (where K = 8C )

dwivedisiddhant03

To solve the given differential equation we have apply variable separation method.

The correct option is (c) 2 sin(4y) - sin(8x) = C.

Variable separation:

In mathematics, variable separation method used to calculate the partially and ordinary differential function in which we rewrite the equation so that two variable occurs on two side.

Given:

The given differential equation is as follows,

[tex]\dfrac{dy}{dx}=\dfrac{\cos(8x)}{\cos(4y)}[/tex]

How to calculate the Separate the variable?

Separate the variable.

[tex]\cos 4y \:dy =\cos 8x\:dx\\[/tex]

Integrate both side of the equation.

[tex]\int \cos4y dy = \int \cos8x dx\dfrac {1}{4}\sin4y = \dfrac {1}{8}\sin8x\\\dfrac {1}{4}\sin4y-\dfrac {1}{8}\sin8x=C\\2\sin4y - \sin8x = 8C[/tex]

Thus, the correct option is (c) 2 sin(4y) - sin(8x) = C.

Learn more about variable separation here:

https://brainly.com/question/18651211

Otras preguntas