(4 points) A Bernoulli differential equation is one of the form dydx+P(x)y=Q(x)yn (∗) Observe that, if n=0 or 1, the Bernoulli equation is linear. For other values of n, the substitution u=y1−n transforms the Bernoulli equation into the linear equation dudx+(1−n)P(x)u=(1−n)Q(x). Consider the initial value problem xy′+y=−6xy2, y(1)=−7. (a) This differential equation can be written in the form (∗) with P(x)= , Q(x)= , and n= . (b) The substitution u= will transform it into the linear equation dudx+ u= . (c) Using the substitution in part (b), we rewrite the initial condition in terms of x and u: u(1)= . (d) Now solve the linear equation in part (b). and find the solution that satisfies the initial condition in part (c). u(x)= . (e) Finally, solve for y.

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)