Solve the initial value problem

y′′+3y=0

y(0)=1
y′(0)=1

The solution is

Step-by-step explanation:

The question is:

Solve the initial value problem

y′′+3y'=0

y(0)=1

y′(0)=1

Step-by-step explanation:

First, we will write the characteristic equation, which is

Then, we will solve for

becomes

∴ or

or

Hence,

Since the two roots are distinct, that is,

The general solution is

Then,

Then, for

Now, from the question

y(0)=1

y′(0)=1

Then,

Then,

........ (1)

Also,

Then,

....... (2)

∴

From equation (1)

Then,

Hence, and

Then, the solution becomes

constants mean the stopped points or the points on a graph that nothing is changing, hope this

step-by-step explanation:

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it