Question

1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli...

1) Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

x dy/dx +y= 1/y^2

2)Consider the following differential equation.

(25 − y2)y' = x2

Let f(x, y) = x^2/ 25-y^2. Find the derivative of f. af//ay=

Determine a region of the xy-plane for which the given differential equation would have a unique solution whose graph passes through a point

(x0, y0) in the region.

a) A unique solution exists in the region consisting of all points in the xy-plane except (0, 5) and (0, −5).

b) A unique solution exists in the regions y < −5, −5 < y < 5, and y > 5.

c) A unique solution exists in the region y > −5.

d) A unique solution exists in the entire xy-plane.

e)A unique solution exists in the region y < 5.

Math   Calculus   
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