if (x-y)^3=A(x+y) ptove that (2x+y)dy/dx=x+2y

Question

Could anyone help me with this question, I just dont know how to proceed?

Answer 1

Just take derivative fromboth sides and then plug in instaead of

A=(x-y)³/(x+y)

 

(x-y)³=A(x+y)

3(x-y)²(1-y')=A(1+y')

3(x+y)(1-y')=(x-y)(1+y')

3(x+y)-3(x+y)y'=x-y+(x-y)y'

(-3x-3y-x+y)y'=x-y-3x-3y

(-4x-2y)y'=-2x-4y (divide by -2)

(2x+y)y'=x+2y

 

(x+2y)y'+(x+2y)dx=0

(A-3(x-y)²)y'=0