Question

3 points
3. What is the solution of
differential eq-(x^4-
2xy^2+y^4 )dx - (2x^2y-
4xy^3+siny)dy =O *
O x^2 + y^4 + siny = C
! O x^5/5 - x^2y^2 + xy^4 - cosy = 0​

Answer 1

Step-by-step explanation:

Let, M=x

2

−4xy−2y

2

N=y

2

−4xy−2x

2

∴

∂y

∂M

=−4x−4y

and

∂x

∂N

=−4y−4x

Here,

∂y

∂M

=

∂x

∂N

So, the equation is exact.

∴∫Mdx=∫(x

2

−4xy−2y

2

)dx

=

3

x

3

−

2

4x

2

y−2y

2

x

=

3

x

3

−2x

2

y−2y

2

x

And, N free of x=y

2

∴∫y

2

dy

=

3

y

3

∴ the solution is

3

x

3

−2x

2

y−2y

2

x+

3

y

3

=c.