If a and b are constants, the solution of (ayaw+b)dx +(2ye KY + axy W -...

Question

Question

math Advanced-Math

Answer 1

Answer #1

Comparing with M dx + N dy = 0

M = a y^3 e^(axy) + b

N = 2 y e^(axy) + a x y^2 e^(axy) - 1

Partial derivative of M wrt y ,

M[y] = 3 a y^2 e^(axy) + a^2 x y^3 e^(axy)

Partial derivative of N wrt x ,

N[x] = 2 a y^2 e^(axy) + a y^2 e^(axy) + a^2 x y^3 e^(axy)

=> N[x] = 3 a y^2 e^(axy) + a^2 x y^3 e^(axy)

Clearly , M[y] = N[x]

Exact differential equation.

Solution is

y^2 e^(axy) + b x - y = c

Answer --> (d)

Hope this helps.

Thanks.

Comment if you have any questions.

Answer 2

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