Question

solve x(x-1)dy/dx-y=x^2(x-1)^3​

Answer 1

Step-by-step explanation:

ANSWER

(x−1)

dx

dy

=2x

3

y.

y

dy

=

x−1

2x

3

dx

y

dy

=

x−1

2(x

3

−1+1)

dx

y

dy

={2

x−1

(x−1)(x

2

+x+1)

+

x−1

2

}dx

∫

y

dy

=∫2(x

2

+x+1)dx+∫

(x−1)

2dx

⇒logy=2{

3

x

3

+

2

x

2

+2log(x−1)+c}

⇒logy=log(x−1)

2

+

3

2x

3

+x

2

2x+c.

Answer 2

Answer:

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