Use the method of variation of parameters to find a particular solution of the given differential equation. Then check your answer by using the method of undetermined coefficients. y'' − 5y' + 6y = 2et

Therefore the complete primitive is

Therefore the general solution is

Step-by-step explanation:

Given Differential equation is

Let be a trial solution.

and

Then the auxiliary equation is

∴The complementary function is

To find P.I

First we show that and are linearly independent solution.

Let  and

The Wronskian of and is

                                                  ≠ 0

∴ and are linearly independent.

Let the particular solution is

Then,

Choose and such that

.......(1)

So that

Now

.......(2)

Solving (1) and (2) we get

   and  

Hence

and  

Therefore

Therefore the complete primitive is

∴The complementary function is

The particular solution is

Then,

and

Therefore the general solution is

the one below it is a function

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough