Problem 1 verify that the differential equation (2x y)dx +(x - 6y)dy = 0 is exact and then solve the associated differential equation

Answer with explanation:

⇒(2 x y )d x+(x-6 y) d y=0

P= 2 x y

Q=x-6 y

So this Differential Equation is exact.

To solve this, we will first evaluate,.

Differentiating with respect to , y

Substituting the value of , k(y) in equation 1.

This is required Solution of exact differential equation.

8

step-by-step explanation:

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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