In this problem, y = c1ex + c2eâx is a two-parameter family of solutions of the second-order de y'' â y = 0. find a solution of the second-order ivp consisting of this differential equation and the given initial conditions. y(â1) = 3, y'(â1) = â3

Step-by-step explanation:

Assuming this complete problem: "In this problem,

y = c1ex + c2e−x

is a two-parameter family of solutions of the second-order DE

y'' − y = 0.

Find a solution of the second-order IVP consisting of this differential equation and the given initial conditions.

y(0) = 1,    y'(0)= 3"

Solution to the problem

For this case we have a homogenous, linear differential equation with order 2, and with the general form:

Where

And we can rewrite the differential equation in terms like this:

And applying the second derivate we got:

We can take common factor and we got:

And for this case the two only possibel solutions are

And the general solution for this case is given by:

Replacing the roots that we found we got:

Now we can find the derivates for this last espression

From the initial conditions we have this:

  (1)

  (2)

If we add equations (1) and (2) we got:

And solving for we got:

So then our general solution is given by:

x=30

step-by-step explanation:

it will cost dollar $540

the living room is 3 which means if we divide 325/3 then we get $108

therefore if 1part of the living room cost $108 and 3 costed $325

then total 5part of the room will cost 5*108 which gives $540