Y= 1/(x² + c)
is a one-parameter family of solutions of the first-order de y' + 2xy² = 0.
find a solution of the first-order ivp consisting of this differential equation and the given initial condition. give the largest interval i over which the solution is defined.

Step-by-step explanation:

We are given that one parameter family of solution of the first order DE

DE

Substitute x=2

Substitute the value of c

Solution is defined for all  values of x except x=

Therefore, by unique existence theorem

The largest interval on which the solution is defined

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

6.9

step-by-step explanation:

simple math really

6 1/2 times 0.6 = 3.9

but if you are just doing 6 and not 6 1/2 then the answer is 3.6