Question

dy
+4x2+2y=é
Solve
x²
dy dy
+4x2+2y=e
dx²
dx
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

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.