Question

answer please....
with solution please.....

Answer 1

Here's your solution
Final result :
Mistake in question :
Replace dx/dy to dy/dx.

x^3=3y^3 sin (x)+ C y^3 where C is arbitrary constant .
i.e y = x /(3sin(x) + C)^1/3

Steps :
1) Convert it in the form of
y' +P(x)y = r(x)y^t where t is real number .
This is form of
Bernoulli’s equation

It be reduced to a linear form by substituting z = y ^(1-t )

2) After reducing to linear form , It looks
like

z' +(3/x) * z = (3/x^3 ) * cos x where z' is dz/dx .

3) This is first order homogeneous Equation .
Integrating Factor is x^3 .

4) Multiply x^3 in both sides of previous equation .

5) Integrate in both sides .

For Calculation Process:
See Attach File

Hope, you understand my answer !